Hi! This is definitely a question your university librarian can answer. Institutions affiliated with JSTOR can choose to offer alumni access, but not all opt for it!
After my last round at university, I got asked if I wanted to keep my university email address and immediately I thought “OH I CAN STILL LOG INTO JSTOR IF I HAVE THAT” so I kept it and every few months they send the “time to change your password” email so the only cost to me is that every few months I have to look at the weirdly designed website and figure out, yet again, how I can change my password.