During last 2(3?) weeks I've noticed that sometimes I've got problem with downloading anything from my library of games on GOG - there is shown error about failed "secure connection" (using Firefox). It's also happening currently - since about 2 hours I can't download anything. This issue is coming back in some random moments - is it fault of GOG's servers, or something else?

(disclaimer - it only happens on downloading, visiting any sub-site of GOG is working correctly)

Troubleshoot the "Secure Connection Failed" error message.

I've already seen that, but there I didn't found anything suggesting that I've got something not right on my side.

Well something's clearly not right. You've been having troubles for a couple of weeks and I see nothing on the forums about GOG having secure connection issues.

I've checked on other browser and on other computer - still the same issue (a bit differently named under Chrome, but still the identical "type").

Then I suggest that it must be something on your network or your ISP's network.

this ^

Random https issues may happen due to unstable connection (e.g wifi). Since downloading the game is more time-consuming process, than loading a webpage - it may be the case.
Or your ISP is trying to intrude your traffic (some of them tend to inject partner's ads). But since it only appears on downloading of games and not anywhere else - chances are low.

I'm rather sure it's nothing in my browser settings, I've checked on two different internet connections, two different computers, different web browsers (used even one which I didn't use earlier, so there shouldn't be any "cookies issue"), I've got no issues with downloading from any other site than GOG.

Anyway, I've decided to use GOG downloader and it went fine, so I've found some workaround.

Plus, I've tried today (with downloading via web browser), this time it went fine. So I'm even more sure that there was something on GOG's side.

i cant post my own topics anymore on Gog. I can post them but they dont show up for everyone to see. Only i can see them.

I did a little bit of research for you and discovered that GoG use a different SSL certificate for their downloads domain (cdn-hw.gog.com) and their main site (www.gog.com). Not sure why. However the fact they are different, does make it plausible that one is working for you and the other isn't.

Here are 3 things you should check:

1) Make sure the date/time on your computers are correct. If they are not correct that can lead to connection failures.

2) On this forum click the green padlock icon, then the large right arrow button ( > ), then check that it says "Verified by DigiCert Inc". It should do.

3) Go to this URL: https://cdn-hw.gog.com/secure/ (their download host) Then do the same as the above: green padlock -> arrow -> check it says "Verified by DigiCert Inc".

403 - Forbidden

That message shouldn't stop him from completing step 3. After the message appears, he should have a green padlock icon next to the address bar that he can click (as instructed).

Checked. Both were fine (but I think that both were good all this time since I had "greened" padlock icon earlier as well.

But I think that I'll start next time (if this issue would appear again) with your advice (checking if protocol is verified correctly)