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.
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