Why does the sound of an old nylon fiber guitar base string on the guitar become suddenly "livelier", or "brighter", after being loosened and then retightened back to its normal tuning?
hmm ... loosening and re-tightening breaks loose accumulated finger crud so that the string can vibrate more freely, allowing more overtones??
Otherwise, I'm stumped! (I play steel strings, so I have no experience to draw on.)
Can you convince us this effect is not in your head? And by "base", did you mean "bass", as in wound strings? If this happened with the unwound strings it would be even more mysterious ...
I'm not sure about this specific case, but some polymers have a tendency to crystalize somewhat after being stressed. Could it be that the elasticity of the string has changed?