Hello, @Lozit, and welcome to our Netlify community site. 
Is it possible that the issue is related to the service worker on the site?
If unregistering the service worker doesn’t fix the issue, then more information is required to troubleshoot this. Would you please make a HAR file capture of the issue and then send that to us?
You can private message (PM) that to one of our support staff and I’ve confirmed that PMs are enabled for your community login. Note, that only one person can see the PM and this will likely mean a slower reply than posting the information publicly. Please feel free to reply to however you prefer though.
It might be best to make the HAR file in a private browsing window and, even then, double check the resulting file for private data before sharing it publicly (or privately for that matter).
If there are any questions, please let us know.