Error: "mod_fcgid: can't apply process slot for" makes my server unresponsive for a period of time
There is surprisingly little information about this error out there.

My server provider suggested that FastCGI might be a poor PHP interpreter for potentially high traffic websites. I switched my interpreter to NGINX with support of PHP-FPM. 

I dont have enough data yet to confirm that freezing was solved completely (but now it wont be related to FastCGI), NGINX is the preferred option for maintaining high performance server as suggested by various sources.