All cronjobs finished after I moved them to new time of execution. All is OK.
No issues. STRANGE
I am currently running mprime torture test. Again all is OK.
I remembered this extremely strange thing: I had a problem with one of my other servers. It was running Debian and every morning at 4 the internet connection to it used to go down. I noticed that it started since I put a mobile phone next to it. I removed the phone and the issue was gone.
So now this same phone was near the other server. I removed it again and hopefully the problem will stop happening.
I will report. But don't put mobile phones near servers.