As the previous poster mentioned, PolarisMail meets all or most of the requirements. (I don't know how to evaluate "Likely to be around for a long time.")
I have been particularly impressed with tech support. I have usually emailed support, and George personally responds almost immediately. When I was getting started, he actually called me on the phone to walk me through synchronizing with Microsoft Outlook (the client which is part of Microsoft Office). There is also a phone number to call (I haven't used it), and an online chat thing which I used once with instant response.
They offer several standard web interfaces: Roundcube (which I like), Atmail, Horde, Squirrelmail, and (for Enhanced accounts) GroupOffice. Their IMAP is very fast and rock solid.
They and their servers are located in Canada (Montreal).
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