If you are watching a channel on Live then it will drop out when you are transitioning to a show that you have set to record. At the end of the recorded show it also drops out.
The 4-tuner Tablo did this if you selected the show but did NOT do this if you selected the channel (by moving to the left of the grid). Even selecting the channel the 4th Gen Tablo has this problem.
When you are watching a channel it should NOT drop out of showing it just because you happen to also be recording something on that channel.