Not sure what to suggest as far as their responses go. That's pretty lousy.
You don't indicate precisely which of the partners you're using for hosting. If I may suggest, I am using Hostek for my hosting and I absolutely love them! No BS, quick to respond to email requests for support, always by the phone when I call, and up to date with at least 99% uptime. And I'm using shared hosting, so it's not too expensive.
I was trying to avoid being specific about the hosting partner, because not sure how many of them even offer a shared hosting plan (sandbox). There is no question that we will be changing host sites, probably going to VPS. Considering AWS as well. It's just bad timing to move at the moment, getting ready to launch major release upgrade. Thanks for sharing your experience with Hostek - I will put them in the mix.
Just move to AWS. You get the benefit of $12 domains, great DNS, free - auto renewing ssl certificates, various os options, various resource options, various drive options, application firewalls, load balances, and only pay for what you use. You can be up and running in LTE to a day.
I've also used AWS, but not for CF hosting. If you are more hand off and just want inexpensive and reliable hosting, I recommend Hostek. If you like getting your hands dirty and full control, AWS is a great choice.