I've dealt with a problem with the ability to highlight text for a while. The problem usually goes away on its own. What I do when it happens is make random key strokes (Esc, etc), and close the document and reopen it form the library. Presently, I'm not able to get the ability to highlight back in my current document. The ability just cut out on me in the middle of the document.
I have researched this on Google, and I see many complaints about this going back to at least 2013, and not a single complaint contains a solution. Adobe apparently doesn't care about this problem.
I am locked in to this product, as I am a graduate student at a university, and the e-books we have access to via the university library require Adobe Digital Editions.