There's multiple issues with TiVo apps currently which they're supposed to be working on fixing.
Having said that, you may have signal issues which won't be helping matters or your box may be on its last legs. Ring up and speak to faults, get them to check the signal levels and they'll send an engineer if necessary.
If your issues are due to the ongoing network problems, speak to them about getting a credit on your bill for the loss of service and inconvenience caused.
The network cable unplugged message is misleading and doesn't usually refer to your own internal cables. It's saying it can't get a connection to the Virgin Media network.