Complaint tracking on My Virgin Media is unreliable - many people (including me) have found that they see nothing on there, even though a complaint has been submitted and is being handled. I suspect the complaint has been accepted and you'll get a response in due course.
However, don't get your hopes up - VM will point you to their interpretation of the relevant "automatic compensation" arrangements, and under these nothing is payable if there was planned work notified in advance, and even if that doesn't apply, there's what Ofcom call a "Payment Trigger Time", and this means VM are obliged to pay nothing unless the fault remains unfixed at 11.59pm on the day two working days after the fault is reported by a customer. With VM's telephony often serving up a recording "we're aware of a fault in your area and working as fast as we can to fix it, estimated fix time XX:XX on day/date, thank you for calling" before automatically disconnecting you, then in those cases there's a good chance they'll insist they had not been notified.
All of which means that the likely outcome is that your complaint will be fobbed off. If you've had three weekends without service, that needn't be the end of the matter, because repeated minor faults or loss of service can be a valid basis for complaint. If you get fobbed off and aren't happy, you can reject the resolution when it arrives, asking for a deadlock letter and you then escalate to the industry complaints adjudicator, CISAS. CISAS will look at your complaint, ask VM for their version of events, and if they uphold your complaint, will offer you a resolution which in most circumstances will be as good an offer as you'll get. Don't forget the onus at CISAS is on your to explain the problem and present a case, and to set out the outcomes that you want - compensation, fault investigation or whatever. The process is an "adjudication", and that's a quasi-legal dispute resolution process that's intended to ensure that customer complaints in regulated industries can be dealt with professionally without the consumer having to take the matter to court.
If you do feel the need to involve CISAS, I would have guessed the most appropriate basis of your claim is that a residential service that is repeatedly unavailable across weekends is not fit for purpose, and does not meet the requirements of the Consumer Rights Act 2015, which requires all services to be provided with "reasonable skill and care". If your situation were a single two-three day outage, or even the odd day on a couple of weekends, then you'd have a very poor case, and CISAS would likely say that VM had not acted unreasonably and no compensation was payable.
And finally, don't forget the importance for you of keeping things in proportion - it's hugely irritating when you have an unreliable connection - but if it's now working, how much effort and time do you want to put in to complaining, and the formalities of escalating? There's times when it is best to accept that the experience has been poor, leave things as they are, but to remember this when your fixed term contract is at an end.
