Well after my last post above and doing the removal and reset which was advised on page 1, I gave it a test. Hulu ran for quite some time on a different channel. Then I tried DIY channel and it would run for about 9 minutes the drop back and actually restart my roku every time. This happened over and over again on the DIY Live channel, till I finally managed to change to another live channel, then it would stay connected. I put on the FX channel and that has been playing solidly for over 20 mins now with no glitches. After my last reset it was difficult to change live channels as the system was very laggy and not responding to me.
Is your Roku lagging or responding poorly on other apps? A reboot of the Roku might be in order.
Next, if the reboot behavior is limited to select channels within the Hulu With Live TV app, it might be worth looking at when it happens. A lot of live content contains commercial breaks. Is it happening at or during commercial breaks? If so, then something about the ads they're feeding could be the issue. Commercials often come from different sources than standard programming content, so if there's something screwy going on at the source, that could be causing the reboots. This has been reported on other non-live apps, and might be what's going on with you. Just something to look into regarding when it's happening.