Do you mean correspondence games or live games? I rarely offer draws in correspondence games because I usually prefer to play the game out to the end and practice endgames.
Personally, I think that any more than one or maybe two draw offers in a game is probably excessive, but it's hard to give rules of course as it's a matter of judgement. Given that, I don't think there's any need to keep track of the number of offers made IMO.
I dont like to offer too many draws during a game and dont like for my opponent to make too many offers either, as they are annoying. When I play here though I often find that I dont know how many offers I may have made in a particular game because track isnt kept of draw offers. Would this be difficult for chess.com to implement ?