Yesterday I was playing in an online rapid tournament on chess.com and we arrived at a position where I could give a perpetual check but not a repittion of moves - because my opponent's King had a choice of two squares to go to. As my opponent had more time than me ( 6mns vs 5 mins) he proceeded to repeat a position twice and then push his King to the alternative square, repeat twice again and then go to the former square etc etc. We did more than 40 moves this way and I expected a pop up to advise a perpetual check situation and declare the draw but it did not happen. Apart from the poor sportsmanship showed by  my opponent, isn't this a draw by perpetual check or am i mistaken?

Should have had a draw window pop up....draw by 3 move repetition doesn't have to be 3 consecutive moves, they can occur at any time during the game.

A draw by repition must be claimed by clicking on the draw button after a position has been reached for the third time. 

After 34.Qf7+ you have reached the same position (with the same player on the move) for the third time - a clear draw!

Moreover, with two more checks (moves 78-79) you would reach a "fiffty-move rule" draw. It would be interesting to see if it would be enough for a draw.

Yes I did claim a draw but it was declined by the opponent.  IN fact I was surprised that he had a say in it!!

Please note that in actual tournament play (on the board) draw by repetition should be pointed out by one of the players. If no one claims it there is no draw even if the arbiter or anyone watching the game see it. I guess that's why chess.com makes us press the claim draw button.

You have to claim the draw after the position has reached the third repetition.

Once you "claim" it on here by pressing the draw button, does the system grant the draw or must your opponent 'accept' the drawn position as a draw?

If it is a valid claim the opponent does not have an option.

Thank you sir!