Input Source Switching no longer working

I have in the past used a keyboard shortcut (command-z) to switch between three different input languages (English, Hebrew, Greek). Recently, however, my macbook is only allowing me to switch input sources when I am currently in situation where I can type (e.g., ready to type in a url-box, with a document open, etc.). As soon as I am no longer in a situation where I can type, then my input language automatically switches to English.

For example, if I have typed a Greek word into a text box but then click away from the search box, my input language reverts to English. Furthermore, If I have clicked on a part of a webpage where I do not have the option to type I am unable completely to switch input languages.

This is extremely frustrating since when I use an online Greek lexicon I need to revert to Greek input every time I need to search a new word.