The solutions here would include switching your email to a more enterprise-level solution. For me on my own company site, I recently went through this same thing, and I wound up switching to a VPS hosting plan.
This means that my email is still running on InMotion's data center, except isolated on my own container. Compare with owning a townhouse.
The other option would be to switch your email over to something like Office 365 or Google Apps for Business (Google Mail). There are pros and cons, the pro is an even beefier system to run your mail. The con is they charge $7/month/user whereas I can run hundreds of mailboxes on my InMotion VPS.
I personally went with a VPS because I've got 5 or 10 other sites that I can run on the same container, so it's a cost savings for me on the web hosting side. But I went down this road because I was having "email deliverability" issues a few months ago.
For you and looking more at just email issues, I'd be considering how many mailboxes you want to use and for how long, etc.
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