To be exact about it, a bacteriostatic water vial, once pierced, is conventionally treated as good for 28 days refrigerated, and that is the limit you should respect unless you have specific data otherwise.
The failure mode is bioburden accumulating faster than the benzyl alcohol suppresses it, which happens if the initial inoculum is large or the environment is filthy.
Worth being precise here: the timeline after opening is: zero to 24 hours is almost risk-free, 24 hours to 7 days is low-risk if refrigerated, 7 to 28 days is acceptably low-risk if refrigerated and handled correctly, and over 28 days is guesswork.
Published pharmacopeial standards specify the use and limits of benzyl alcohol in preserved presentations.
The practical summary: use bacteriostatic water for multi-withdrawal, store refrigerated, and respect the 28-day limit.