Multipath is when the broadcast signal bounces off nearby hills, buildings or other objects. Te result is you get the original signal directly from the tower and one or more multipath signals that arrive a split second later. In analog TV the "later signal" would show up as one or more faint images to the right of the main image - hence the word "ghosting" in the analog world. In digital, multipath confuses older digital tuners that don't deal with multipath well, resulting in dropouts in audio and video.
Different lengths of coax will affect multipath problems, which may explain why the longer coax receiver is working ok. As cusemax said, you may need an attenuator on the shorter length of cable. Wind, weather, temp and humidity can also affect multipath. It can vary throughout the day, and from channel to channel.
The best way to solve the problem is to:
1: Get a better (NON-TERK) directional antenna that can focus on the main signal from the tower and null out the multiple bounced signals arriving from other directions (multipath).
2. Get a newer digital receiver like the DirecTV H20 that has better multipath rejection. The DVR version of the H20 will be available later this year.
I would get a better antenna -
anything but a TERK. For specific antenna recommendations, post questions in the thread for the city you live in
HERE. You'll get answers from folks in your area.