I do not believe this is a CSS issue. On my site I have other pages that have this same form that are not in the accordion and there are no problems.
The accordion has css and your form control is inside the accordion so it could be affected by the accordion's css. Before we look at sources of the problem in JavaScript we need to ensure the source of the problem is not in CSS.
As to step 3, this will be quite difficult since I would have to link a database to the the form. It will be better if I showed you the site and you could see the issues there.
We can't work on an issue without confirming that the issue exists completely separate from your system, other than the minimal circumstances and steps required to reproduce it. That means creating a simple page outside of your system that has only three things on it (from your description):- A jQuery UI Accordion
- A form inside it
- A select box inside it with values (one pre-selected)
That can and needs to be done without your system. It's a bit of html and css and javascript, no database or any other back-end required. It's essential that this page have on it nothing that can be removed and still have the issue present itself. Then we open that minimal test page in IE9 and can prove that the issue exists in the jQuery UI Accordion. Until then, respectfully, we have to assume that the issue exists in your system, because that's the only place it's been seen.
You're saying
A. my select box works inside my page
B. my select box doesn't work when it's inside the accordion
I'm saying
A. your select box works inside your page
B. your select box doesn't work when it's inside the accordion inside your page
Where we need your help is to be able to say
C. your select box doesn't work when it's inside the accordion NOT inside your page
The fact that the select box has no issue inside your page doesn't alone prove that the problem is in the accordion when that accordion is also inside your page.