"How does one know that one is just not cut out for Aikido?"
I fear I'm showing a lot of hubris to answer this question -- there are teachers here who will answer far better, and I am a raw beginner. But as far as I could figure from my experience, you'd ask yourself:
Do I love doing aikido?
Do I feel a rush when just this once, by accident, I move correctly and the energy flows and the movement and the throw are effortless...?
Do I find repeating the same technique again and again to learn a subtle improvement worth the practice, or do I get bored?
If the answers tend toward "yes," then it seems to me that you're right for aikido.
It sounds to me like the problem isn't aikido, or even the testing schedule. It's a nagging fear that there's really something wrong with you that the sensei isn't telling you and they're deliberately keeping you from testing. Maybe it is time to sit down and have a quiet talk, just to clear the air. If there is something wrong, Sensei should have told you by now. If not, you need reassurance that you are OK.