The bare-bones OS that runs on a VS normally has to share a number of VS spreading the tick cycles between the allocated processors and the total volume of RAM in the bare bones OS. This means that your site could be getting dragged down by the overall number of VS's that run on the system; eventually the shared resources may run tight.
Have you asked if GoDaddy will provide what aspect of your site is high capacity? Can you validate the Apache logs to see (depending on how the logs are configured) what load exists on Apache. Maybe your running out of Memory? It is important to know why your site is 'over-capacity', how else are you going to know what the appropriate configuration RAM/Space/# of processors, RAID configuration, Controller... that you need if you do decide to move it?
Maybe think about using one of the 'Pay per use' options that Amazon EC2 (free for 1 year promotion currently running) or Windows Azure. Theses services you can tune with growth and don't have to think about it in terms of having to move servers as you grow the cloud platform is more flexible that the traditional blade VPS configurations and can grow and be tweaked to your site needs.