then the upgrade to a new router would be beneficial in the long run.
However, unless you subscribe to one of those cable companies that sell you the modem and do not charge a "modem" fee, the onus to replace the modem is down to them and not to you.

It would appear as though your wireless modem is using 802.11n, currently the fastest wireless speed available, but they do tend to wear out over the years.
Replacing it with an newer one may help your problem. Fortunately, they are relatively cheap.

The problem here is which component is causing the problem. The wireless Router is the Gateway, which you say fails a couple of times each day, but you also say that you have to reboot everything to get back on line.
Have you tried just rebooting the router?
During these failures, are all the correct lights lit on the Surfboard modem?