To load data from an API data source, I am using an approach just like described here. However, if I attempt to perform an UpdateContext in the OnVisible event from the very first screen when the app is loading, it never works. If I create a "Screen1" with a simple button that navigates to "Screen2", and put my UpdateContext in the OnVisible of Screen2, it works every time.
So: doesn't work when loading the app, but works fine when navigating.
The only other clue I've found is this: just for kicks, I decided to try looking at the app on my phone to see if the Screen1 OnVisible would behave differently. It still didn't work, but it did give me an error message about how I can't make a data call when not logged in. ?? Naturally, the navigation to Screen2 still worked just fine.
So, that suggests to me a timing issue. It's running the OnVisible before the app is prepared to actually make an API call.
It also suggests that we could improve the PowerApps Studio if it can't tell me about an error but PowerApps on my phone can...