Ok, so lets start here: right when you hook up the box and you lose a signal from full power stations, the issue most likely is your antenna. This happens because some stations broadcast in analog in the VHF band, a simple VHF antenna—like rabbit ears—can pick up the signals.

Here’s the catch: if the station’s digital signals are in the UHF band, then rabbit-ear antennas won't be able to pick them up.  To solve this problem, simply get a VHF/UHF antenna (rabbit ears plus a loop antenna) to pick up both digital and analog signals. Keep in mind reception is also based on where you live and where the TV is in your home. If the issue still goes unresolved, try an outdoor antenna. Depending on where you live and where your TV set is in your house, you may need an outdoor antenna.

Before you do all of that though, weigh the option of all you will spend with those antennas and then just getting a new TV with a digital tuner built in? Something to think about.  

Finally, there are antennas that can only receive UHF stations and ones that receive both UHF and VHF signals. If you are rather certain you won't want to get any lower channels in the VHF channel 2-13 range, you could purchase a UHF-only antenna.