Hey CA3LE, thank you for all the information! I checked the cord that hooks into the cable modem. It looks good. Don't have a wall plate for that cord, it just comes up from the floor. The cable company ran another line to the cable modem back around the time we first got cable internet. Thankfully the cable company here is really, really good about not charging for service calls. Only time I have had them charge us was when we asked them to install a new amp for the line that goes to the TV's.
I really appreciate you taking the time to put together all that information. I'll let you know how this all turns out. So far it has been close to 3 days since I have had to reboot the modem. If it keeps happening I'll have the cable co come out next week.