If you do not feel comfortable with a hosting provider, it's up to you to pack up your data, databases, and domains, and move it over as a precaution to another host so you can switch on a dime.
If you have a contract with a business that states they are responsible while you pay for upholding their part of the deal, being providing support and service, and they are lacking - that sounds like a reason to stop paying.
Perhaps that there are circumstances for the owner of the company - but to be honest, they are responsible and have a responsibility and should reach out to their customers.
Again, if you are not feeling right with where you are hosted, there are thousands of alternatives that do give you a better spot.
At the very least make a working offsite backup of your sites. Make sure You are the owner of the domain(s), and take preventive measures
