@Corsair:
Umm interesting. Now try to register on my dev demo site and see if you have the same problem. Its strange how you can log in like after a certain time. Id say your cookies and browser cache settings may be the cause of it:
http://www.mysidiaadoptables.com/mys130b/index.php
@Pokepet:
The old Mys script? What do you mean by that? You are talking about your old adoptables site made with Mys v1.2.x or v1.1.x? What version were you using? I thought you had a customized rusnak script...
And yeah, your host can possibly do that since you may be using too many database queries, tables and rows. Contact them for info and see if it is the case.