For the last two weeks I've been on the phone with our web host almost every day, mostly dealing with email problems. As you can imagine, this is a terrifically good use of my time. The problem is that we're on shared web server sending mail through a shared mail server. Because shared resources are, well, shared, our web host (whom I very much like) is fanatical about protecting them from abuse by a single customer. It turns out that we generate enough traffic and, especially, enough email that we are abusive just going about our normal business.
The solution, then, is to move to a dedicated server. I'm actually excited about this, but it will take time, and time is, if I haven't made this point recently enough, something I don't have much of right now.