Hub stats look OK to me and no evidence of the hub rebooting in the log posted. If it was rebooting then I'd expect to see an entry with a date stamp of 1970 on it. A tiny rise in Pre RS errors is not going to impact your connection, those are errors the hub has seen and been able to deal with.
What happens to the lights on the hub when you lose the connection?
As you are in modem mode, do you have your own router or just one device connected to the hub in modem mode? If you have your own router the first thing VM staff will ask you to do is take it out of the equation to rule it out as the culprit.
My setup: VM TV box, M350 Fibre broadband with Hub 3 in modem mode connected to a Netgear R7000 router. Telewest/VM user since 2001.
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