watch out for other wobbles
Their DNS service has been wobbling for ages. reg-123 (and its other brands) are those that tend to have huge advert in magazines. They appear to work on attracting huge numbers of customers so they can afford to lose customers when they eventually get fed up with the service.
As for staying with them simply because you have renewed, that's like saying you'll keep driving your car cause you've just paid for the mot/tax disc even though it breaks down regularly. Bite the bullet, get setup somewhere else, get everything moved and then cancel your account. It will be a lot less stress and hassle in the long term and probably save you money as well when you take into account your time spent dealing with issues and lost business.