String material will make a difference in how stable the string is, but that's just one factor.
New strings, even when pre-stretched, will generally settle in some.
Lower strand counts will stretch/creep more.
Heavier draw weights will cause more stretch/creep.
If you unstring your bow, when you re-string the brace may settle in some after a little while or after a few shots--especially with a Dacron string, but also with some others.
Hot weather will cause a string to stretch/creep more, especially Dacron and 100% HMPE (UHMWPE).
Materials with Vectran (BCY-X, 452X, 450+) will be the most consistent in all conditions.