After playing around with the Billion 7800NL I managed to sort out something that solved my problem.
It appears the default setup doesn’t include any sort of QoS, so I played around and managed to create some rules which see to be performing what they should.
It wasn’t running out of connections, it seems to have just been starved of bandwidth at various times. Post those QoS rules being done, it’s now been stable for over 5 days. So that’s made me quite happy.