Strange thing. We are running 3 websites on Fusion template. All of them with CF7 contact forms, on all of them the form stopped working few weeks/2-3 months? ago.
1st site is +6 months old. 2nd site is +3 months old. And on both of them initially CF7 worked (configured email recipient address received form messages). 3rd site is a brand new one (created ~1 month ago and since beginning the form on this site is not sanding email messages. All sites are placed on the same web server under different domains.
This last example shows me that pottentially it is not the issue of spam blacklisting our domains (freshly registered domain, never used before).