If there's a persistent issue on a particular unit, definitely report it. In theory, it is all monitored remotely but that doesn't always catch everything. The TOC themselves have little to no technical/troubleshooting access to the equipment, so you'll need to contact the operator - most of them have a dedicated support email per TOC. GWR use different providers on different stock so you'll need to contact the appropriate one;
Icomera (gwr.on.icomera.com):
[email protected]
PassengerWiFi (gwr.passengerwifi.com):
[email protected]
Just drop them an email saying what unit you're on and what the problem is. Most other TOCs will also have the support details on their sites. It's the sort of thing where if no one reports it, they're not aware there's a problem. There's a few I reported during the early days of Southeastern's deployment that got fixed as a result.