Goodaltgamer: I must admit i have only seen it once, but I do keep my GOG cookies. I know of one case where keeping the cookies did avoid the recapture.
That used to be the case a week or two ago when GOG made the captcha appear more often. That caused problems to many, e.g. with gogrepo.py tool you couldn't use the "login" option anymore to get valid login cookies, but you had to import the cookies from a browser for gogrepo (you had to do this only once though, once you have valid login cookies you can repeatedly use them from there on).
However, GOG seemed to silently change it back (due to all the complaints I presume). At least for me gogrepo.py login command works fine again, and I don't get captcha even though Firefox clears cookies automatically.
Goodaltgamer: BUT, it might also have to do with the 2 step feature, maybe you only get the recaptcha if you don't have(had) it?
No I don't think so, I just tested it and as far as I can tell having the 2-step verification enabled or disabled doesn't trigger captcha, at least I am not seeing it.
A long time ago I recall getting captcha when I was testing something with my account, repeatedly logging in and out of my account many times in short time. Then I suddenly got the captcha IIRC.
EDIT: Or it might have been that I was testing the two-step authentication actually, to see in which cases GOG sends you an email of someone trying to log in to your two-step auth enabled account. So I actually repeatedly tried to log in both with wrong password, and the right password, to see when I get those emails. So it might be it was the wrong password entries that triggered captcha (which would make sense to me, to stop brute-force attempts to crack accounts).