What sort of compensation should I be trying to get for two months of intermittent Internet?

The auto-comp scheme

https://www.virginmedia.com/help/billing-and-payments/automatic-compensation

only covers a 'total loss of service' for phone and/or broadband.

VM will argue you won't qualify for anything if you have an intermittent or degraded service (even if the degradation is so bad as to make the service unusable).

You would need to put in a formal complaint to VM first of all to demand VM compensates you for the poor service and failure to repair (which, in all likelihood, will be fobbed off)

https://www.virginmedia.com/help/complaints

before escalating to the ombudsman via the timescales and processes below

https://www.commsombudsman.org/our-process

You will need to collect evidence of your poor quality connection so set up a BQM to track your connection 24/7

https://www.thinkbroadband.com/broadband/monitoring/quality

Also speak to Citizens Advice on how to proceed as there will doubtless be other aspects of consumer law which apply if VM is failing to give you the service you signed up for.

You are unlikely to receive a reply from the VM forum team here in ‘Tech Chatter’. A VIP or moderator might move your topic to a better forum, such as ‘Managing Your Account – Cable’ to get a VM reply.

Do you have a BQM running? That monitors your connection 24/7/365 and provides a pretty graph that demonstrates the stability (or otherwise) of your broadband.

That provides good evidence in situations such as this. https://www.thinkbroadband.com/broadband/monitoring/quality 

If you don't have one, spend 5-10minutes setting one up now.