That symptom could be various things. To know what to blame, you would want to know whether the pressure switch was sending power to the pump, and the pump was not delivering water, or if the pressure switch had a delayed closing (turn-on).
If what you describe is predictable, I would suspect that either the well is running out of water, or the pump motor is shutting down due to overheating.
Where is your pump? Down the well (submersible) or up top?
Yes. Zero water pressure results in no water in the tank, unless the tank has failed.