Android - Android phone constantly loses Wi-Fi connection

I can't say that I completely understand how but the issue was solverd after I changed the DNS settings of my phone (for my home WiFi). I set it to Google default DNS 8.8.8.8 and 8.8.4.4.
And since that never this problem again.

Why the phone was loosing the whole connection is still unclear to me (though it remains now pure theoretical question)

Depending on the version of android you are running you can try going to System settings> WiFi> Advanced> Tap "Keep Wi-Fi on during sleep" and select "Always"