Heavy load, MYSQL down, FCGI with too many proccesses... need help

In the last week my sites were down almost every day. Sometimes 10 minutes, sometimes 4 hours!

The support is not able to give me a final answer, so I am searching someone with experience that could help me on this! It is very frustrating… I started with DH in 2006 in shared host, and as I was growing, I was upgrading, but it seems to not help. =(

Right now I am under Half Moon plan, but I would even upgrade further if this would help. But the support says it is not something they can assure… =/

Should I move some sites to DreamPress? I run basically many wordpress sites, with caching system, some even with cloud flare! Have no idea anymore how to improve.

Thanks for any help.