Tennis balls bounce because the air pressure inside is higher than the outside pressure. They begin to lose bounce as soon as removed from their pressure can. The alititude where the ball is played will affect the bounce. As they are played, they lose more bounce. Typically, they lose too much bounce to play after about 3 sets of recreational (amateur) tennis, or 8 games of professional tennis.
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If you open a new can of tennis balls and leave them in the can without using them, it can take a week for the tennis balls to have a significant loss in their bounce.
If you are using tennis balls daily, then it can be a matter of a couple of weeks to around three weeks until the tennis balls lose their bounce completely.
After about 3 sets of recreational (amateur) tennis, or 8 games of professional tennis.