Ever since i have owned my computer, my modem has never been turned off, except in an electrical storm. it runs day and night and works as perfectly as the first day i turned it on. some people leave thieir modems running day and night and some people turn them off. i can really see no harm in running mine 24/7, except for the small amount of electricity it uses each month. its just a personal choice.
The design and manufacture of these devices has advanced to the point where it should be lasting longer than you can practically make use of it. I’ve been using the same modem since 2002, and it has only been shut off on special occasions, and never for any sizable length of time. It works just fine.