Can taking the same set of strings on and off several times change their tone?

I definitely think so. Go get a bendy piece of metal and bend it back and fourth a few times and watch it snap. The constant stretching and contracting can't be good.

 

Is like boiling. No negative reflections on the time you keep on rebecoming for little brilliant. But as all the consumable things they decade with use.

 

IME: depends on the string and how carefully you handle them when changing them out (multiple times). also: lots of folks cut their strings way to short for the first installation (they really don't need to have that "three windings" look*) and that alone will bear upon long-term viability and the re-use of the string.

bottom line: use your ears --- if they sound good/competent after every re-installation = no problem! good luck with your string changes!



* looks are for kids!

 

I would be worried about metal fatigue of the core of each of the strings from winding and unwinding the string around the tuning posts. Did you straighten out the leads of the strings each time you removed them, or did you let them stay rather curled up. Yes, I know you must have had to straighten them a little bit to get them through the bridge. So it is breakage, rather than tone, that is the real concern.