Shoulda, woulda, coulda...doesn't mean the battery WILL last. Never count on it, because as often as not...it won't. That battery may be long in service and due for a deep cycle...at the next inspection...tomorrow. You might not have noticed the failure right away. It may be partially gone. You may have a cold soaked battery that's not going to give your full figure...Remember that battery requirements are certification requirements...not necessarily what the aircraft will do in the real world. Just what it's been demonstrated to do, for type certification.
The duration of the battery is very much dependant on multiple factors, not the least of which is the load under which it's operating. A ten ampre-hour battery, for example, will provide one amp for ten hours, or ten amps for one hour. In theory.
Same for backup power supplies.
If you're seeing an electrical problem, you may be seeing something you don't yet know about. Loss of electrical power or fluctuation might be a short that's starting a fire...it might be a control failure that will cost you all your electrical, including battery power. It may be a number of things...don't count on being able to fall back to battery. Often with electrical things, you're seeing the tip of the ice berg, and the problem that manifests isn't the real problem. This can be especially true of a shorted item on a bus affecting other items.
Most of the time a problem can be traced to a grounding issue. That sounds simple enough, but it can be a bear to troubleshoot...something you don't have the luxury of doing (and shouldn't do) in flight, even with test equipment, wiring diagrams, and maintenance publications in a well lighted shop. Additionally, a ground can present as any number of problems...and a short is a ground. You may have bigger fish to fry than loss of a generator, a popped circuit breaker, or the duration of your battery power.