If your site is using a lot of resources and has lots of visitors, you can get more reliable service by purchasing a virtual private or dedicated server.
If your site is small and your just starting out, no reason to spend all that money -- a shared hosting account will be just fine.
If your site keeps going down, then it's time to switch hosts or confront your host about it. It's best to use an uptime monitoring service, such as Pingdom, so you have concrete data on when and how long your site is down or if the response time is too slow. Then you can ask your host about it and show them the report.
~Sovereign
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