I added the VPN based on my experience, so I couldn't have made a mistake on that. Don't forget that we have different VPNs, and you don't expect them to always behave the same.
No, VPN is not the reason OP browser will be login him out of this forum, that is not possible and I am 100% certain about this.
Initially, I wasn't even referring to the VPN as the cause of the log out in my initial reply, but part of the reasons that the captcha-solving issue could take longer. But now that you've added that you are 100% certain about VPN cannot log an active session out, you couldn't have been more wrong.
First, you don't personalise the experience and use it to conclude for everyone, as you do not know the kind of VPN the person is using, and neither do you know their browser, the extensions there (including the private/VPN extensions) and the general settings of the browser. Only the OP can answer all that. I've read complaints from forum users about the misbehaviour of their accounts in such a manner. Is yours behaving like that? That means you can't speak for everyone, even if it doesn't happen to you. Some issues could be technically personal.
Now, aside from the possible settings I listed above, VPN may cause a session mismatch with active cookies. This means that it will not delete the cookies from the browser or intend to do so, but it could cause a misread, and thereby log the person out. Because this doesn't happen all the time doesn't mean it can't happen, or become frequent in some cases.