Today when I was reading a ECN post:

We are facing the following issue in our environment. The Content server version is 7.2 on Linux. This environment was upgraded from 6.7 about 5 months back…. bla-bla-bla something about stability and performance…

I have remembered that during last year I had participated in resolution of similar problems two or three times.
Here is a root cause: Randomness in virtual machines (don’t pay much attention to “virtual”)
Why did this happen after migration from 6.7?
The answer is simple: in D7 SSL connections are enabled by default, so, D7 consumes more entropy.
What to do?
Check Marginalia page.