You should only offer one draw unless the position changes significantly, in my opinion you both showed poor sportsmanship.
Players who refuse to draw drawn games.

According to FIDE rules, you actually have to claim the draw after fifty moves with no pawn progress and no taken piece, it's not automatic. Since chess.com has no tournament director, I believe the rule is moot here.
That position still might not be a draw, because according to Reuben Fine about the 50 move rule: "Exception is made only if it is shown that an ending has resulted where theoretically more than fifty moves are required to give checkmate. In this case a number of moves double the number established by theory as being necessary for this object shall be allowed instead of 50." But it seems the only way to prove it would be to actually mate, which would take more than 50 moves.
At one point they changed the 50 move rule a few times for stuff like that; however, they've since changed it back, and even if you have a forced mate, tough luck. This came up a couple years ago where 2 super-GMs had a game that was forced mate in 278 with the first capture after like 252 moves or something. Of course this is by tablebases, and they didn't see the crazy forced win anyway. I'll try to find the link...

What was the final outcome?
I had a similar problem but even worse!
I am playing a match and got the Queen, a Rock and a Kninht advaantage and the fellow is not giving up!!!
It is really annoying!
lol o artista consegiu perder
Well done thats why we should never accept or offer draws even two nights against K you still have to prove you know how to defend correctly... I would delete my account if I would do something that dumb complaining that the game is a dead draw and then giving away a f*c%n* piece just to prove how right your opponent was!

That position still might not be a draw, because according to Reuben Fine about the 50 move rule: "Exception is made only if it is shown that an ending has resulted where theoretically more than fifty moves are required to give checkmate. In this case a number of moves double the number established by theory as being necessary for this object shall be allowed instead of 50." But it seems the only way to prove it would be to actually mate, which would take more than 50 moves.
At one point they changed the 50 move rule a few times for stuff like that; however, they've since changed it back, and even if you have a forced mate, tough luck. This came up a couple years ago where 2 super-GMs had a game that was forced mate in 278 with the first capture after like 252 moves or something. Of course this is by tablebases, and they didn't see the crazy forced win anyway. I'll try to find the link...
Mate in 278?!! I didn't know that was possible! And how would they know without playing it out?

That position still might not be a draw, because according to Reuben Fine about the 50 move rule: "Exception is made only if it is shown that an ending has resulted where theoretically more than fifty moves are required to give checkmate. In this case a number of moves double the number established by theory as being necessary for this object shall be allowed instead of 50." But it seems the only way to prove it would be to actually mate, which would take more than 50 moves.
At one point they changed the 50 move rule a few times for stuff like that; however, they've since changed it back, and even if you have a forced mate, tough luck. This came up a couple years ago where 2 super-GMs had a game that was forced mate in 278 with the first capture after like 252 moves or something. Of course this is by tablebases, and they didn't see the crazy forced win anyway. I'll try to find the link...
Mate in 278?!! I didn't know that was possible! And how would they know without playing it out?
As he said, tablebases. Here's more information about them: http://en.wikipedia.org/wiki/Endgame_tablebase
That position still might not be a draw, because according to Reuben Fine about the 50 move rule: "Exception is made only if it is shown that an ending has resulted where theoretically more than fifty moves are required to give checkmate. In this case a number of moves double the number established by theory as being necessary for this object shall be allowed instead of 50." But it seems the only way to prove it would be to actually mate, which would take more than 50 moves.