Sewing Machine Needle Keeps Falling Out?

I am a novice seamster though I've not had this problem before now. I have a Singer Esteem II sewing machine that is just a few years old. I was sewing up some thick, pinned fabric the other night, was probably going too fast and the "heavy duty" needle came down on the pin and snapped the tip right off.

This wasn't new to me and I set about unscrewing the screw from the needle bar to remove the broken one. I then inserted a brand new Singer heavy duty needle that was exactly the same as the one that snapped. I must have tried twenty times to get the needle up, positioned correctly (flat side facing back) and the screw tightened so I could continue on, but it simply would not. I checked, rechecked, and checked again to make sure it was pushed up to the stop pin, that it was straight and perpendicular to the needle plate and even got pliers to see if my mini screw driver wasn't able to tighten the screw up sufficiently. It was a tight as possible, but as soon as I let go of the needle to see if it was in, it would fall right back out. I even had to remove the plate and fish the darn thing out because it fell through at one point.

Any suggestions as to what the problem might be? I've barely used this machine, have done maintenance regularly and have never had a problem with changing/inserting needles before. Thanks, in advance, for any advice you might have.=0)