I owned several DirecTV TiVo boxes, including a couple of HR10-250's, and I never had a reboot because of signal loss, whether caused by rain, snow, ice, or the one time somebody cut the wrong coax cable. (oops!) It always just showed "searching for signal" or whatever on the screen until the problem was resolved.
TiVo Mini X 3
Left DirecTV 4/15/07. Left TWC 8/8/11. Now on Comcast Xfinity.