You should probably provide more details like logs etc. - otherwise it’s hard to say what your issue really is.
However one thing I can say I experienced recently was issues caused by 2-step login verification – feature on GOG.com itself. Everytime I was trying to login in POL I would get an email from GOG asking to also put in additional security code – but POL doesn’t provide place to put in that code.
Solution was to go to GOG and disable that feature. After logging into your account via web, you can find it here:
Privacy & Settings > Login and Security > Two-Step Login