I reached the same conclusion separately from the author and pretty much by luck. For some reason, my Captcha plugin setting was set on “Captcha v2”, even though from the beginning I’ve set it on v3 (I don’t know the difference, I just know that usually higher numbers mean something is gonna be better :)).
I’ve switched it to v3. It asked me to update the security keys. I did just that. The problem was suddenly gone — no more lockouts for 3-4 days already.
I didn’t suspect the issue was connected to Captcha plugin because when performing compatibility checks before, disabling the plugin didn’t help at all.
Updating the Version to 3 and security keys helped. I don’t understand the reason behind this, but I’m happy I don’t have to reconfigure the site for AIOWPS all over again. I was considering it, but for now, I’ll see if any more problems arise.