I honestly don't know how to explain this, so I'll explain it perfectly.
Sometimes blocks just become invincible from certain angles. By "Invincible", i don't mean bedrock, i mean nothing can hit them. They are still tangible(can't walk through them), but blocks cannot be placed on them, and you cannot hit them.
Sometimes if I dig around them i can hit them from behind/the side and actually destroy them, but It's fairly annoying.
This only started happening recently, and it started right after I started using java 7. I already tried using java 6 again, but the problem still occurs.
Yeah, I get this periodically when I'm mining. It's almost as though it doesn't exist from all but one or two faces. I find if I back up, move so that I see it at an angle (thus, I can see the front and side), and then hit the side at the far edge, it usually works. Not sure why it happens, but it's quite annoying.