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Unfortunately the cumulative windows updates are prone to reset some of the windows settings. I suspect that is what has happened to you. There was another of these updates on 1st March and it is being applied automatically via Windows Update. At the moment we seem to getting one or two per month.
You have an input language in Override for default input method selected. This naturally overrides all input language settings. To make it work as you'd want to you need to select Use language list instead of a specific language, then modify the language list making your preferred language first on the list.
Logics: Selecting different input method (language) for each application uses the language list, letting you to select from installed input languages separately for each app. By overriding the list you tell your system only to use that selected input language instead of a list of languages.
As Windows has been told to override the list, always use the selected language list instead, it does not need to be set separately for each app, therefore that selection is not needed because all apps are using the selected "override" language.
Kari, your trick did not help. Today I've got the same problem again. And I even do not know when this happened. Updates have not been installed several last days...
I have been having the same symptom as you. ("Let me set a different input method for each app window" becomes unchecked)
And I have been choosing "Use language list (recommended)" instead some language.
Until now (2016-06-30), the issue has not been resolved in Win10.
I hope Microsoft can really focus on Multilingual environment. The IME platform is revamped and more secured but is more inconvenient than Win95.