The issue doesn't require a PC to even be attached to the network, in fact it occurs still even when the entire home network is unattached. It cannot be releated to a service which is running crazy with bandwidth. The modem is getting into some state where its stuck and won't recover until a hard reset is issued.
If you own the modem, twc may have given it the wrong billing code and it's getting the wrong config file.
What is the config file? Do they push that from their end? I have two accounts with TWC in two different locations in the state, so maybe that's what the issue is?
you have the correct firmware. What thge billing code does is configures or provisions the modem for the speed you pay for. TWC has been known to send a file for the wrong mfg of modem and they get flakey.