This occurs for two reasons. The first is the guide data provided by the TV network (not Verizon) lists the program ending a minute or two before it actually does. Some networks do this on purpose to encourage DVR users to visit their web sites. This is very easy to get around by changing a setting in the DVR timer to extend the recording time.
The second reason this occurs is if you have two DVR timers active followed by another timer or two (i.e. back-to-back timers). In this case, the DVR must end one of the first timers to start the second timer (or timers). If the program ends after the timer switches, you'll miss the end of the program. In some cases, this is due to the first problem, in others it is simply due to a small time difference between the end time published in the guide and the actual end time. You may be able to work around this by adjusting start and end times, although the best way is to avoid back-to-back timers on programs when this occurs.
I'm not sure it's necessary to have two timers set for it to effect the cutoffs. The DVR only has two tuners. (My version anyway.) If I am watching one show and simultaneously recording one, both tuners are in use. So if there are two back to back recordings scheduled, they would use the same tuner, and timer. Therefore the timer for the first show would shut off before the second recording could start.