When I rooted my phone, I had to restart it weekly as the performance degrades over the course of a week. Before I rooted it and after I unrooted it, I only reboot once a month. Normally, if I noticed something is not behaving properly, that is one of the things I do. More often than not, it was some other issue.
This past month, I had to reboot a few times due to the new 4.3 update on my SGS3. I had a few issues and was trying to reboot it to fix them. It turned out I just had to reinstall some apps and that's it. It has been a few weeks since I've rebooted my phone now.