Place uses a Bennett Pump but with special solenoid assy on it. Test the pump by pulling the plastic cover off and disconnecting the pump power wire from the solenoid loom and energizing it with 12V. Obviously make sure the ground wire is hooked up. If the pump works you have a solenoid problem, if it doesn't you have a pump problem. Tap on the solenoids as sometimes that will free them up. Doesn't fix them but at least tells you what the problem is. I know of no feature that shuts it off automatically for low fluid.
We've had several of these pumps fail over the years. Many times Bennett or Place will warranty them, sometimes not if they're old or abused. If you need help just call Bob or Tom here Monday AM. They're both very familiar with these units. We can also handle any warranty situation you might have if your pump's bad if it's under warranty.