It's true. Omnidirectional antennas are not as effective as directional ones for weaker than local signals. It's also true that you might have a bad coax lead. The coax is easy enough to check with a good quality VOM.
Since terrestrial TV went digital, and you did mention that you now have newer TV's, could it be that your newer TV's just need to be reprogrammed in the spot you are camping in? If not, this needs to be done. The instructions to do so should be in the owners manuals.
The new digital terrestrial TV signal is very geographically affected. Obstructions such as hills, trees, buildings, etc, all will affect your incoming signals from each individual transmission tower. Maybe some stations you were able to receive before are too weak now with the newer system. As stated before, there really is no more weak, snowy, but watchable TV stations. If the incoming signal is too weak, you see nothing. This is where directional antennas excel with incoming weaker signals over Omnidirectionals. But the transmission tower of that particular station is still the the goal to point the antenna toward. If that tower is within range of an omnidirectional antenna, no problem. If not, black screen. Is the whole thing a bit more cumbersome, yes. You can thank the FCC for that. They say they needed the bandwidth for other things.
Regardless, I hope this helps a little. With terrestrial digital TV, you will need to reprogram your TV/digital converter when parked at locations you don't frequent with your current antenna. Even with an upgrade, depending on where you go with your toy hauler, you may need/want to reprogram your TV's at each location. I would try with your current antennae first and see what the outcome is before investing.