Yes, that's the well known IE bug with z-index and select elements. It's been around for years, and I've been dealing with it in one fashion or another for years. A colleague and I worked out a solution using IFRAMEs, but the memory is fuzzy. A web search on "IE select z-index" should give you enough information on the issue to choke a horse.
The select boxes don't "disappear"... in fact, they are always on top; they show up on top of the DIV. They do so even if you give the DIV a z-index of 999 and the select a z-index of -999. It's a bug in IE.
Of course I think you're nuts, amy - but I sense a ban hovering over my head if I continue.
Edit: Not a ban from you... but from
Mr. "You've Been Warned", if I expounded on
why I think you're nuts.