The inverter will run continuously if:
The battery(s) voltage maintains 11 volts(10.5 volts for GO-AC models) or higher (15.5 volts max 16 volts max for GO-AC models).
Sufficient air spacing and ventilation around the inverter
Not unusually high air temperatures (90+)
Wattage is below continuous rating of inverter
To determine how long a typical battery will last we need to find the amp/hour rating of the battery. The cold cranking amps or CCA rating is only a number to compare manufacturers’ batteries. Somewhere on the battery labeling there should be a "reserve minutes" specification. Simply times the "reserve minutes" number by .3 to get an amp/hour rating for the battery.
For example:
What is the amp/hour of a battery with 100 reserve minutes?
100 x .3 = 30 amp/hours**