thats the way they work, the d.e, dead end, is the controller controlling the pump, if you leave it long enough ps will flash up because it has built up enough pressure to activate the pressure switch, when the d.e cuts in, its getting ready to come on instantly when you turn the flow back on.
Have the pump come on for a seconds like it does when the controller is flashing de shouldnt run the battery flat, what size battery are you using?
I though this was a problem when i first got mine, but that is the way they work, both of mine do this, i have 2 pumps and 2 controller running from a 75ah battery as well as a cordless drill wired in to the battery to wind the hoses, and the battery will last 2 days before it needs recharging.