Bill,
Thanks.
Lots of acronyms involved with DOCSIS.
To keep things simple (mostly for my sake....) the key is the T3-Time-out errors shown in the log.
The cable modem has been sending messages out and not receiving replies. Either the outbound message is not getting to your isp (Cox) or the reply is not getting back. It resets itself and tries again for awhile. Your resets may be forcing an early reset that may or may not succeed.
The cause of problem is likely an intermittent failing cable, splitter, or connector along the connection path into your home.
Overall the DOCSIS network communications are being interrupted and your internet connectivity suffers accordingly.
You will probably need to call Cox for support and they should be able to see the problem after a few tries. They may ask you to read the event log to them. I do not believe that the modem itself is the problem but the combined log events may prove otherwise.
Hopefully a technician will be sent to locate and repair or replace the failing components. And/or the modem.
If you are the curious sort just Google DOCSIS and read some tutorials about it all - half the battle is all of the acronyms. Othewise - just call Cox as you are paying for service.