If a paid app stops working, can I get my money back? For example, the application Say it right! is using the Forvo third-party service. I guess the app can stop working eventually (for example if the API changes, or if the third-party service terms change)

Are paid apps purchased from the Google Play store supposed to work for lifetime?

Edit: The previous example costs 1 euro, and obviously if it stops working that would be no big deal. But the same applies for apps that cost 20 euros or more. I wouldn't be happy if an expensive app stops working after 3 months, and I'm curious if Google has a policy for this on its Play store.
Help section of Google Play Store (accessible from Google Play Store menu button on left > help and feedback> search for returns and refunds> Apps and games refunds) relevant to your question, says (emphasis mine)


  After 2 hours or more,Contact the developer
  If Google Play's 2-hour return period has passed, the developer is responsible for deciding if you are eligible for a refund. Contact the app developer directly and ask for a refund. You can find an app developer's contact information listed on an app or game's detail page on Google Play. For instructions, go to help with an Android app or game.


(Edit: 11 Mar 20 - just saw that it is 48 hours not 2 hours to claim the refund. I don't know when it changed) 

So, it's obvious that the refund request approval rests with app developer and if the developer doesn't respond, it further says


  Optional: Contact Google
  If the developer hasn't helped, Google may be able to. Contact our support team for help solving your problem.


Reading between the lines, there is no obligation for developer to refund. Further, no where does a developer give a "life-time" guarantee, for that matter no software can guarantee that. It is simply not possible to do that for obvious reasons.

To sum it up, I don't think you are within your rights to assume and ask for a refund as in your case

Edit: In response to your edit, the answer still is the same, but the developer may be more inclined (guessing) to work on an update and release that to fix the problem occurring in three months, since other users would also be affected and would adversely impact his rating on Play Store, which they are quite sensitive to. Mailing him in this case may be the best option, with app /system logs and crash logs if any