yes; performance will diminish by playing; but you can’t really generalize about tape signal quality degradation as there are many variables. and also the question is at what point is this degradation audible?
modern tape formulations hold up better, properly maintained transports, and better tape paths are easier on the tape.
i have tapes i’ve played on my Studer A-820 master recorder dozens of times without apparent degradation. but the quality of the tape, and the transport quality is at the very tip top. this is 1/4" 15ips. all of my tapes are high quality modern formulations, most are at least 10 years old.
i’m sure there would be measurable degradation, but so far i don’t hear it for my playback purposes.
lower speeds, and less robust transports, less quality heads, less quality tape, will have different results.
to answer your question; playing a tape 3 to 4 times should not appreciably diminish the playback quality unless the deck has problems. most (but not all) 30-50 year old decks have some level of problems.