Do you leave the heating cables for the roof/ gutter on 24 hours a day?
Probably not, but...

You'll need to read the literature that undoubtedly came with your heat cable (or, at a minimum, share with us what product you're using). Generally, they shouldn't be left on continuously, and they shouldn't be on when outdoor temperatures get above 30 degrees F, give or take. What cycle you need depends on the local climate, current weather, installation technique, and other factors. 

Lots more good advice here.