Nope. As I read it, any token less than a week old would work. So for any user, they have 7 * 24 * 60 tokens live at any time.
I've seen people on PureGym's Twitter successfully refreshing screenshots weekly though, and the API response suggests the same.
That being said, I couldn't find a validation endpoint to check if mine got invalidated by something specific (maybe signing out?) or if there's some other magic happening.
My gym has a similar system but I realised it's time based and the app functions without Internet. I installed the app onto an old android with no sim, logged in at home over WiFi and it successfully regenerated QRs without data