Press-on nails should be removed as soon as they start to chip or the nail no longer adheres fully to the nail bed. This can be recognized, for example, by hair getting caught underneath the nail.
If the nails are left in this condition for longer period of time, water can seep underneath them and moisture can cause mold to form. The nail can also detach unintentionally, damaging the natural nail bed. If the nails were applied correctly, chips should begin to appear after a few days in the case of adhesive tabs application or after approximately two weeks for glue application.
You can learn how to properly apply and remove press-on nails here.