I have not had either of our H3's shut down due to losing an OTA signal. However, there are funky things ONE of our H3's does (such as frequently becoming UNlinked to its H3 after it is off overnight at least 3 times a month), while the other H3 NEVER loses its Link. There are other buggy things ONE H3 does that the other H3 NEVER does.
Be aware that all these bugs are NOT universal to all H3's. Often it seems only some H3's. I do not know why, but it is what it is.
In your case, the shut down would STOP recording any shows that are recording until the H3 finished rebooting, and the recording with several minutes missing can be frustrating (almost always to my observation, the H3 will record the next airing of that interrupted recording of the show--if it is available like 3 hours later or later in the week, but there is a chance that show may NOT air again soon).
If this troubling behavior becomes too much of a hassle, you can try to force a software download to get the latest and see if that helps, or if you don't want to wait for the next release of an update to the H3, you could request a replacement H3, but be aware you would lose all your recordings unless you transferred them to external HDD before sending it to Dish.