Hi Michal,
Clearing the browser cache sometimes works with this issue. Otherwise you can try this workaround:
1. Start Mendix Studio Pro
2. Wait for 10/20 seconds and double-click on the Mendix Logo in the top left corner of the open window.
3. Select Create New App (this will open Studio Pro)
4. Go to Edit -> Preferences -> New Features -> Disable the 'Browser sign in' option
5. Close Studio Pro
6. Start Studio Pro and sign in with your Mendix account as you would normally do.