those cable modem log entries are OK.
On the modem, just ensure that the SEND and RECV lights are on when you are having trouble.
My cable modems (Time Warner) respond to this, from your browser (despite the subnet differences)
192.168.100.1
And if that yields a web page for the router, look on the SIGNAL tab (or some such name).
The downstream (from cable network) signal should something like -10 to 0 dBmV. It won't vary much. It'll depend on how many splitters are between the modem and the cable entering your home (keep it to one two-way ahead of the modem).
The upstream signal is problematic: it will vary according to noise and loading and weather. Should be a number between about 40 and 50dBmV. Look often. If it gets to 55 or more, that means the upstream (modem to network) is marginal. If it stays long at 55 or 58 or so, the SEND light will go out and your modem has "lost synch on the upstream". Again, keep the number of splitters to one two-way between the main incoming coax and your modem.
This is for the DOCSIS 2 standards in modems, which is service at up to 20Mbps or so down and 1-3Mbps up (often, limited to 1Mbps up by the ISP).
D0CSIS 3 is in a few systems, with faster speeds, higher prices.
Hopefully the ISP, not you, owns the modem. The ISP can interrogate the modem signal levels. Watch the upstream in the evening busy hours and when the weather is unusually warm. That seems to adversely affect the cable plant infrastructure and cause signal problems.
The key though is the number of splitters and avoiding 3 way or 4 way splitters in the path to the modem.