No simple answer - too many variables involved, such as original tape, storage conditions (e.g., temperature, humidity, air quality), and playback equipment condition.
With good well maintained gear, substantially more than your ~15 plays, but each playing adds the risk of mechanical problems (machine decides to eat the tape) and wear.
http://www.amianet.org/sites/all/fil...t_sheets_0.pdf provides some qualitative information.
Best approach is to convert original to other media that can be reproduced without further losses and play the copies
I have tapes from as much as 36 years ago that play OK, considering the quality of recorders and off-air source material back then, but I do not play then very often.
And for multi-play testing purposes, use expendable tapes, not material you want to preserve. Play the important original stuff only when you really need to.