Spotlight search on iOS not showing options to search web/maps/App Store unless it has results from other apps I am noticing something both on my iPad 2 and iPhone SE running iOS 9.3.2 that I don't recall seeing until today. When I do a spotlight search, it shows a list of results from different apps, and then at the bottom options to search web, App Store, and maps. But now, if the search is such that there are no results from apps, it won't show those last three search options either.

Also, if relevant, a search that brings up just one top hit of an app and nothing else, also does not show options for the web/app/map search. Also, spotlight might start showing a result, like of a note I'm typing, but as I keep typing just a little more of the title of that note, then all results disappear.

And when offline, this problem goes away. Even about the disappearing notes search result problem.
Upon a little testing around, I have discovered the solution. Go to Settings > General > Spotlight Search and disable Bing Web Results. There must be some problem either on Microsoft's end or in the way the iOS software gets it, and this interferes with Spotlight from doing what it needs to do.

Hopefully Apple will fix this and it can be re-enabled with iOS 10 or a future iOS 9.x update, or it will be fixed on Microsoft's end, if the issue becomes known to them.

It's unclear to me if this affects everyone or just a small number of users. If you're not sure if you have this problem, test it out as per the original question. And please comment if this does or does not fix it for you.