I installed Gog galaxy, and everything was ok for couple of days. But one day I couldn't open the gog galaxy window. I checked in task manager, and the program was still running, but I just couldn't reach it. I uninstalled it, and make the new installation. I found all installed games, and everything was ok for another few days, but now it happened again.

Does anyone had similar problem or know how to fix this?

Cheers

I don't know how to fix it, but I would definitely contact support. They might be able to help you.

Right click and end task?

Instead of contacting support, there's a sticky about the software that the developers pay attention to and monitored. May want to bring up the issue there:

https://www.gog.com/forum/general/gog_galaxy_official_discussion_thread

May also want to skim the last few pages of that thread to make sure you're running the most recent release as they've kicked out a few in the last week or so.

Hope this helps

Fortunately, it isn't required for playing GoG games.

Have you run virus checks etc? Seems odd that software works for a few days and fails. Any patterns to when it fails?

there was an issue with the recent GoG update and AVAST thinking it was maleware, thusp putting it into the Quarentine
No matter what you did AVAST kept putting it back into Q. So I deleted AVAST and wnt with Kaspersky. for me problem was resolved, eventualy there was a thread on the forums that said that AVAST resolved that issue with an update, but with as many false posatives that AVAST seems to find I got fed up with the software.
Check your Antivirus quarentine chest first, then if you still can't find GoG, contact support.