The popup reminders that appear upon login can be snoozed to make them reappear at a later date.  Critical reminders can only be snoozed until the due date.  Other reminders can be snoozed indefinitely.
What determines if a reminder is critical and thus prevents snoozing beyone the due date?
If your club sets a particular date or condition as one that will suspend a user from scheduling, then this date is considered critical.
What if my club does not want to suspend a user for a particular date (e.g. BFR) but they do want to prevent snoozing past the due date?
You can do this by checking the suspend checkbox on the User Date Limits screen and entering a grace period of 999 (days after expiration). This actually gives the user 89 years after the expiration before they are suspended, which in effect will never suspend if there is a real date in these fields.