That would be the modem side, not the router. You can verify this next time it happens by checking to see if you can still access the router with your browser, or see other devices on your network.
No. It does not suggest that. It could easily be the cable to your modem and/or the cable "drop" entering your home. You sure don't want to spend money on a new device only to have the problem still there because the problem is the cable somewhere.
So first, make sure the coax cable is securely connected to your modem, and not damaged. Typically, with cable internet there will be a splitter (similar to a Y connector) in the coax cable somewhere with one side going to the modem, the other feeding cable TV to the rest of the house.
If you don't have cable TV, you want to come directly from the ISP to your modem. That is,
no splitters, no splices. One solid cable from the drop where the cable enters your home to your modem.
If you have cable TV too, you want the smallest splitter necessary feeding your modem from your ISP. That is a single "2-way" (1 input, 2 outputs) splitter, one side going to the modem, the other feeding the rest of your house for your TV(s).
Some older homes may have 3-way or 4-way splitters or even have multiple splitters from the drop to the modem. What is critical to note is with every split, the signal strength from the ISP is divided in the splitter(s) even if the other sides of the splitter are not being used. TVs (or cable boxes) don't normally have a problem with that. But modems like a very strong signal strength.
These splitters may even be hiding in a closet, the attic or basement or on the outside of the house, exposed to the elements. If possible, follow the cable from the modem all the way back to where the cable enters the home. If there are splitters, check to ensure all connections on all the splitters are tight too. Note the splitters located outside can go bad over time as they become weathered. Inspect the labels on the splitters. If you encounter a 3-way or 4-way splitter, but only need a 2-way, replace it. If you don't need a splitter, remove it and (for now) use a
barrel connector. Eventually, you should replace the entire cable to get an uninterrupted run, if possible.
Also, if you live in an older home that was wired for cable TV long ago, the splitters may be outdated - designed for less bandwidth than needed today for cable Internet. If you need to use a splitter and the current one is old, I recommend one rated for at least 2000MHz or one like
this one.
For now, next time you experience this problem, I recommend you contact your ISP. They can check the line to your modem for proper continuity from their end. You need to verify it really is your modem before spending money on a new one.