Um... if by "drawn position" you mean something like "stalemate, or the 50 moves rule", it's insta-draw in those situations.
Repeat Moves In Drawn Position

Taken from wikopedia:
How to draw
1) position repeats 3 times:
In chess and some other abstract strategy games, the threefold repetition rule (also known as repetition of position) states that a player can claim a draw if the same position occurs three times, or will occur after their next move, with the same player to move. The repeated positions need not occur in succession. The idea behind the rule is that if the position is repeated three times, no progress is being made.
In chess, in order for a position to be considered the same, each player must have the same set of legal moves each time, including the possible rights to castle and capture en passant. Positions are considered the same if the same type of piece is on a given square. So, for instance, if a player has two knights and the knights are on the same squares, it does not matter if the positions of the two knights have been exchanged. The game is not automatically drawn if a position occurs for the third time – one of the players, on their turn to move, must claim the draw with the arbiter.
ok so basicly if the position of all the pieces on the board repeats itself 3 time you can claim a draw.On chess.com IF you press the request draw button AND there the position has repeated itself 3 times you will get a draw automaticly.
2) STALEMATE
stalemate ie you cant move any piece except your king and your king has no legal move then its a draw
3) 50 move rule
The fifty-move rule in chess states that a player can claim a draw if no capture has been made and no pawn has been moved in the last fifty consecutive moves (fifty moves by each side)
4) draw by agreement .. for example you cannot force checkmate with king + 2 knights V king .I have actually won a game when i only had a king vs king + 2 knights because my opponent refused my draw offer and timed out:) or wrong colored bishop and rook pawn vs king can be draw if you get your king in the correct position
5) all pieces are exchanged with only kings on the board - it happens- draw insufficient material.

Fifty move rule and Threefold rule are hard to keep track of and rarely used, so most friendly, casual or informal games ignore them.

According to my last game after offering draw using draw icon it was rejected. Then I actually repeated draw position 11 times with opponent . The system was timing me down during this charade and I realised that "the system" would not accept a draw automatically, Potential result lose on time !!
Draw In This situation: King moves in only two allowable positions while being checked each time.
As I was in a weaker position this was my best stategically created result
My only conclusion is maybe I must hit draw offer countless times until system switches in to do it automatically.

It should be noted that the above was in "the middle" game with many pieces on board and not an end game

According to my last game after offering draw using draw icon it was rejected. Then I actually repeated draw position 11 times with opponent . The system was timing me down during this charade and I realised that "the system" would not accept a draw automatically, Potential result lose on time !!
Draw In This situation: King moves in only two allowable positions while being checked each time.
As I was in a weaker position this was my best stategically created result
My only conclusion is maybe I must hit draw offer countless times until system switches in to do it automatically.
You want to hit the draw button after ANY position is repeated 3 times. (It doesn't have to be three times in a row). Understand, it has to be the exact same position, even a simple pawn move will kill this kind of draw.

How many times can a repeating drawn position be allowed before an automatic draw occurs....
By the laws of chess there is no automatic draw for threefold repetition. The site handles it this way. http://support.chess.com/Knowledgebase/Article/View/40/0/how-do-i-claim-a-draw
"In online or turn-based chess, once the position is repeated three times, make your move. Now, on the screen for that game, just below the notations box there will be text for you to click on that says "claim game". Click on that to claim the draw."
Note you have to claim before your opponent moves. This can be difficult in live. Seems the programming could be changed so you claim the draw after your opponent repeats the position not after you do.

you have to manually click draw. if the position has repeated three times, it'll auto-draw the game after you click the button.

That makes sense. So the difference is when clicking draw option, opposition can accept or reject. But when checking position has repeated three times or more and you click draw the opposition has no ability to choose and it then auto draws.
Hope this is right for next time.

The rule is 50 moves without a pawn advance or a piece capture.
Otherwise, other ways to Draw is by agreement, insufficient material to mate, stalement, or threefold repetition.

i just finished a game, where this player repeatedly checked me at two spots and forced me to keep alternating my king position. i seemingly was at stronger position in terms of material and positions and the system forced a draw. feels like i was cheated out of victory isn't it prerogative of the checker to change his move over the checkee?????

http://www.chess.com/livechess/game.html?id=316045638 - for reference.

ravio84:
How can you say you were in a stronger position if you left your king vulnerable to just this type of tactic? Why should a player be inclined to play anything but the move they consider best? And if the best move is to force this kind of draw, then why shouldn't they pursue it?
Material and piece activity aren't the only things to consider when evaluating a position. If your king isn't safe, then that's a big negative if your opponent can capitalize on it, even if it is only to cause a repetition.
Edit: I should also point out that the system didn't force a draw, the player did. If the player hadn't claimed the draw, the game could have kept going.
ravio your position isn't strong if the opponent can keep you in check.
In your position you had an option out of the checking pattern anyway so your stubborness caused the draw instead of the win you likely could have obtained from just moving Kg8 and continuing on.

Oh! @omnipaul i concede, that my king was vulnerable. and i did say seemingly stronger (maybe only by material) but i was forced a draw by the system through the players moves, i always considered that if the person who is repeating checks should change his moves, as the onus is on him to get the game going. can i get credit for bad sportsmanship from his end? or he did the right thing and forced a draw?
I too, played hoping he'd change his tactic and that point in time i considered those moves ideal.
Also" thanks for the time to look through the game. i just wanna make sure i understand the nuances and not make the same mistake again
Oh! @omnipaul i concede, that my king was vulnerable. and i did say seemingly stronger (maybe only by material) but i was forced a draw by the system through the players moves, i always considered that if the person who is repeating checks should change his moves, as the onus is on him to get the game going. can i get credit for bad sportsmanship from his end? or he did the right thing and forced a draw?
I too, played hoping he'd change his tactic and that point in time i considered those moves ideal.
Also" thanks for the time to look through the game. i just wanna make sure i understand the nuances and not make the same mistake again
The responsibility to stop the repetition is on whichever person does not want a draw. If stopping the repetition would put either player at a disadvantage then likely neither player would wish to stop it and the draw would happen.
In your case you could have stopped the draw and been in a better position than your opponent which means it would be on you to stop the repetition and it would be on him to try to keep the repetition going to get the draw since he was worse off.
There is absolutely no bad sportsmanship in causing repetition.
How many times can a repeating drawn position be allowed before an automatic draw occurs.After draw was rejected I repeated the drawn position 8 times before realising that eventually I would time out.