Should run continuously once the engine has started, just runs for a short time when you switch on the ignition to prime the system.
It's a constant pressure system with any excess fuel being relieved back to the tank.
If the fuel pump relay is getting very hot then it may be on its way out or the current draw is too high. You can check the current draw of the pump, Haynes manual gives you some figures to work with. Excessive current draw could be blocked filter (go for that first) or impending pump failure.