Unfortunately this is a very common problem and there is nothing you can do to fix it. It's less common on the newer V6 box but it can sometimes happen on those as well. If you have broadband with Virgin, do consider swapping to a V6 as it's a much better box than your current TiVo and much faster. You will lose the recordings on your TiVo.
No not at the moment, or at least not as a straight box swap with no other changes. They run promotions from time to time. The biggest ran from January to April last year, and they were offering free swaps to all customers.
The best thing to do is speak to the Retentions team if you haven't renewed your contract in some time, and tell them you're fed up of overpaying for outdated and slow equipment and you're thinking of switching to Sky. They should offer you a better deal with a V6 included, and you'll probably end up with a lower monthly bill as well. To reach this team, ring 150 or 0345 454 1111, and follow the prompts to "thinking of leaving us" followed by "technical issue". This will put you through to UK based Customer Services/Retentions.