I'm not saying your site wasn't down, but please make sure it is really down the next time it appears to happen. See this blog article for simple ways to check if your site is actually down, or if perhaps you just have connection issues:
Is your web site down? Maybe, maybe not.
How to test your web site. Tips if you think your web host is down | Official WebHostingBuzz Company Blog
It's surprising how often someone thinks a site is down, but it turns out that the site is up for other people but there is some routing issue on the wider Internet or with that person's ISP.
As for e-mail blacklists, that is an ongoing problem on shared hosting. Usually a server's IP(s) get blacklisted because another user account on that shared server was spamming, either consciously or due to an insecure script. I admit that WHB hasn't always been pro-active about blacklists, and it's been necessary to inform them of the blacklisting. There are web sites on which you can periodically enter your server's mail-sending IP and the tool will check it against multiple blacklists. If your server is on any major blacklists, send the information to WHB Support and they will take steps to have the blacklisting lifted, once the offending account has been dealt with.
I am not WHB staff and I am not paid.
I provide help in these forums on my own time.