In addition, which recording mode are you using? (I assume that you have a standalone DVD recorder.) XP/HQ/Fine? SP? LP? EP/SLP?
The "disc stopped recording, it is full" message indicates that you've tried to record more video than the disc can hold (at a given recording mode). As such, you cannot finalize the disc because there is simply no room on the disc to do so (according to the recorder). The result is that you have a "coaster."
In addition, some brands of DVD recorders default to HQ/XP/Fine when you first plug it in - and that highest-quality mode will record only one hour of video on a single 4.7GB disc.
Finally, some 2-hour shows actually run a few minutes over 2 hours. DVD recorders give you absolutely no leeway at all whatsoever to accomodate such overrunning because a small amount of blank space on a disc is required for finalizing.