You should try to get more details from the hosting company on what the problem was. If it was just a massive spike in traffic (e.g. "farked" or "penny-arcaded") there typically isn't much you can do about it outside of paying massive amounts to prevent that kind of problem.

If you're exceeding traffic limits or hitting their database server too hard then those can typically be solved by going to a dedicated server, since typically if you are hitting something too hard on a shared resource the provider will typically throttle you (Usually breaking something in the process).