Ok, so here are the two dangerous moments of a power outage when dealing with HOB
First, when the power shuts off, the line from the pump to the display tank can reverse siphon and actually overflow the sump. Solution: Drill a small hole in the return line at where you want the water to stop draining if the pump shuts off. This will allow air into the line and break the siphon in the event of a power outtage.
Second, when power comes back on, if the siphon has been broken in the overflow box, the pump will simply fill the DT up until it overflows, and then burn itself out. This is where design and craftsmanship comes in. Is your HOB
OVerflow box home made or purchased? I have an Eshopps and I've already tested it numerous times. Starts back up like a champ.
Third possibility. If the flow through the oveflow's U-Tube is not fast enough, air bubbles may build up in the bend and eventually break siphon, leading to the same result as the above paragraph. So periodically check your U-Tube to ensure there is no air collecting. If there is, it may need to be cleaned, or check for snails and whatnot slowing the water down.