Thank you very much Peter Verbeek! I disabled the task from Task Scheduler and I'll see if that helps in the next startup & logon. Strangely, there's no shortcut to UpdateChecker.exe in my startup folder but I found the file in C:\Program Files\EqualizerAPO. I'll create an exception in TinyWall for that.
I updated Equalizer APO and Peace, after that every time I restart my computer I get a "error while checkin for update" "permission denied" banner, after logging in to Windows. I have unchecked "Check for a newer Peace version" but it doesn't help. I do have a third party firewall, TinyWall, where I've set C:\Program Files\EqualizerAPO\config\Peace.exe to have unrestricted access to internet. Any tips what to do next? Is there some other component that needs an internet access?