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.
Very stuck from the situation. This problem happens randomly and in the version 10.12.1 is not present Disable the 'Browser sign in' option.
There are others alternative in order to resolve the problem ?