I spent 2 years in a Visiting Assistant Professor position, which just "ended" after 4 tenure track positions were filled. I was not considered for any of them. My best guess is that I a) don't have enough research, 2) am older (definitely 40+) so won't be there for long enough. After the semester, the Chair called to ask if I would like to stay as a Visiting Assistant Professor one more year to teach Statistics, which I am not good at so said no thank you. Yesterday, I accidentally received the minutes from this week's department meeting which state an "request to fill" position was just approved, so they will be "rush hiring" for that this summer. Should I contact the Chair to let him know that I am interested? Or let it go? I am confused as to why I couldn't be considered. I hope it is not an age thing...
I have been on many faculty search committees and helped with hiring of VAPs. I have no access to mind reading abilities to see what's inside the skull of the hiring committees who did not "consider" you (your words.) So let's start with the basics:
Did you apply for the other 4 Tenure Track (TT) positions? If you did not apply, they didn't consider you, even if you made a verbal expression of interest.
If you did apply, then they probably did consider your application and decided against you. At my department, we guarantee VAPs that they'll move to the second round, but that's obviously not your department's policy. For those 4 TT positions, were they for Assistant Professors in your area of research?
You mention that you have little research. VAPs are teaching positions, and it's very difficult to do research with a full-time teaching load. Are the TT positions previously open research-based, i.e. they expect you to get extramural funding? If so, there's your answer. You should apply to teaching-based TT positions. There are many out there.
If they considered and decided against you, it could be the age thing, but I doubt it. Again, I have no insight about what went into their minds, but we hire people in their 40s and 50s all the time.
You also mention that they just got approved a "Request To Fill." Is it for another VAP position, in statistics, the one you rejected? Or for a rush hire of a TT position? To me, it sounds like a rush hire of a VAP. If that's the case, you already rejected that.
To answer your questions:
Should I contact the Chair to let him know that I am interested? Or let it go?
If it is a TT position and your research is within the scope of the advertised positions, yes, apply. A formal application is the only way to know if they want someone like you.
If they don't call you for a second round (short-list/phone interviews), then it's time to move on.