Distinct possiblity that there is some sort of unrecoverable error on the HDD or the connection to the splitter, and each time the DVR gets the error, it doesn't handle the error very gracefully.
The other thing to try is to swap the location of one of the STB's with the DVR, and see if the problem stays in the same place, or follows the DVR. It it stays in the same place, it is a connection problem, and you probably need to re-seat the connector for the coax both at the DVR end and at the splitter.
If it follows the DVR, it is probalby time to get a replacement DVR from Verizon.