Unfortunately, there is no set standard or answer in this case. There are a lot of factors to consider when assessing a panel's standby and backup capacity. Age of the battery, temperature, size of the battery, even the load imposed by the system's operation as well as if you're pressing buttons all factor to standby times.
As a general term, most home alarm systems will provide at least 4-8 hours worth of standby time, with the general consensus of systems exceeding that time. If your system is programmed for an extended (greater than 4 minutes) bell or siren timeout, as well as have a large power load upon alarm condition, the system will drain the standby battery faster in AC loss, standby in-alarm condition. A frugal use of bell output load and reasonable times can increase the standby time significantly.
Of course, unless a proper standby and alarm load calculation is done, there is no way to estimate the total standby time your system is capable of, as well as routine battery replacement and servicing to eliminate what is the weak link in this case.
As stated in other articles here, an aged system battery will provide some power upon loss; however upon placing a load for a period of time, will fail rather quickly.