The ear training thing does sound frustrating!
I can remember a time when my results would have been like yours. These days I could ace that sort of test without thinking. That said, I'm not an expert, and I've never done any music teaching, so take my random ideas as just that:
- I assume you've already heard the song-association advice. (Find a common song that starts with the interval you're learning, etc.)
- I know how easy it is to feel like surely this one exercise is something you've *got* to be able to do, and shouldn't be *that* hard, and to just be bullheaded about keeping at it. But maybe it's time to step back, try a different ear-training approach for a while, and come back to these interval identification quizzes in a month or two?
- Singing is another way people usually come at this. Have you tried stuff like: play a note, see if you can match it with your voice; play a note, see if you can find the major third above; etc.? Or there are plenty of sight-singing methods out there, you could pick one up and work through the exercises.
- If you're open to trying technology, I'm rather fond of "functional ear trainer" (free ios/android app) and "meludia" (online subscription service, but I think you can try some of the exercises free). They both take a different approach.
- Ear training is one of the things music departments do every day, so if there's some way to sign up for a course near you, that might help. They'd have the advantage of a tested curriculum, teachers that can answer questions, fellow students to collaborate with, maybe labs with software you can use, etc.
- Hopefully Anthony Wellington could make some suggestions too.
Keep at it! In my experience it is normal to hit plateaus and not make progress for a while. But any progress is very rewarding in the long term!