To reproduce:
1. Open attached project "APIUpdate"
2. While Unity is opening focus on any other app (you need to make it before API update pop-up will appear
3. Notice that API update pop-up won't come to top or in any other notify you what it is required
4. Mouse over Unity logo, it will only show Loading bar making you think that it's simply loading instead of requiring your action

Same for upgrade pop-up.
Quite annoying issue with big projects as you never have Unity in focus in those cases.