This is occurring due to a loss of connection to the power source. Here are the 3 things to check.
If using the TRB External Battery Pack from Night Goggles: There is a black plastic insert that connects the Anker Battery inside the case to the cable connected on the outside. This black insert needs to be firmly seated into the battery. After some use, I actually super glued my insert (to the inside case-not the battery) because after years of use, it can get a little loose.
If using CR123s: The battery door may seem tight, but it may not be securely closed. Make sure it securely snapped shut all the way around. It could be this or a set of batteries that isn't fitting correctly. Some CR123s have a longer positive terminals and can cause issues if not long enough. In rare case, it could be a spring issue not creating enough pressure in the battery compartment. I would try a different set of batteries and make sure the door is tight.
Mount: The Hogsters are rated up to a 308, so a .223 shouldn't be an issue. However, I talked to one customer who was having this happen and after troubleshooting, he asked me if it is normal that his scope has some play in it. When I asked what he meant he said his scope wiggles a little bit. Number one, it would never be able to hold zero like this, and number two that extra play/wiggle was causing a fairly violent shake every time it was shot, and again causing the scope to turn off. When you mount your Hogster, adjust the tension adjustment on the right side of the mount, so it is so tight that you can barely get the locking handle closed. Many picatinny rails have different tolerances. For virtually every Hogster I mount mine on, I have to adjust it to get it to fit perfectly.
If none of these three items corrects your issue, then I would contact Bering optics at 817-453-9966 or at sales@beringoptics.com.