There's also a check valve in the system to prevent water from being pushed back down into the wall. If that leaks, the pressure (air pressure from the bladder) will just push the water back out of the tank. If the pump is turning on/off without using water in the house, that may be bad. Have you watched the pressure gauge? When not using water, it should stay constant, essentially forever. If the pump had just run to fill up the tank, and there's no more water use, it should stay there. Now, if someone uses some water, it should slowly and smoothly drop until it gets to the point where the pump low-pressure switch turns it back on to try to pump the tank back up to the upper limit. Depending on the pump and how much and how fast you're using water, the pump might stay on while you're using water, but when you stop, it should rise to the upper limit and turn off and stay there.
As said, you can often tell if the bladder in the tank is shot by knocking on it...if the tank is full of water, it will sound different than if the bladder still has air in it. Part where the bladder and air are will sound more like a bell, the part that has water in it will be more like a thud. If it sounds like a thud everywhere, buy a new tank! If the pressure drops when you aren't using water, you need someone to service the check valve, or you have a leak in the pipe somewhere in the well, if you can't see water anywhere else.