Wild Wild West? Sounds like your fleabytes.com might be a godaddy or wild west domains reseller.
In regards to RegisterFly, many registrars helped to support the effort of moving domains out of there. Godaddy helped, enom helped, etc. RegisterFly was the first ICANN accredited registrar to ever lose accredidation as far as I know.
nudu: If you register with a domain reseller and the reseller closes up shop, the registrar usually has a master account for this reason. All domains would be sent to the master reseller account so you could continue to manage the domains.
In regards to a registrar closing up shop, they should give you enough notice about the situation at hand. In most cases if a registrar cant afford to stay open, another company may buy them out like with what happened with Stargate. Stargate was a registrar and decided to no longer offer registrations. So they sold their domains division to another company and the customers continued to do business under the new company.
Any quality registrar will always give you a heads up of what is going on. Also remember that you are the registrant of the domain. So if the registrar goes kaput and you still have 3 years left on the domain, I would imagine the registry and ICANN would take over the situation in some way to make sure you can continue the registration period elsewhere.
You could also probably get a better explanation by reading your registrar's terms of service agreement and reading some literature on the ICANN website.