It seems if you disable interrupts on your processor that is handling your video drivers for too long that it will cause problems with the video output, presumably because the drivers would not know when a frame has completed. Initially you might think that as long as you disable interrupts for less time than it takes a frame to complete that you would be in the clear (~1/30th of a second for NTSC), however since the processor does not necessarily have control over when the frames come in (i.e. the video is asynchronous to the processor), this is not the case. Because of this the interrupts would have to be disabled for less time than it takes for the video ports to go from the end of one frame to the start of the next.
In the case of NTSC, if we assume there are 525 lines in each NTSC frame and that 480 are considered active video than the time between frames should be the time for 525 - 480 = 45 lines. Since NTSC is operating at 30 fps we can assume that there are 30 * 525 = 15750 lines being drawn in a second so each line should take 1/15750th of a second or .000063492 which multiplied by 45 would be .002857 seconds or about 2.86 ms. So for an interrupt disabling to potentially cause a problem with the video drivers it would have to be longer than ~2.86 ms.
However if you think about the double buffering that should be in the driver this should not really be a problem either, so we would be back to interrupts needing to be disabled for over 1/30th for a frame drop. If this is the case, why would having interrupts being disabled for relatively short periods cause frame interrupts?