Drop down z-index issue?

We are chasing an interesting issue and was hoping you could help. We have a real estate client where we are using a real estate plugin to feature their in-house listings (the plugin is called RealtyNA).

The client has asked us to add a search form to the top of the various sector pages of their site which we have done. The issue we are running into is that the drop down menu for Property Types wants to go below the content that is in place below it. Here is the link to the page in development: http://traddcommercial.com/sector-page-search/.

The search form is in a different Color Section than the content below it and we have tried applying z-indexing to no avail. What is odd is we find that if the search form is within the same column, the under-lapping issue goes away (as evidenced on this page which is all contained within one column: http://traddcommercial.com/properties/).

My suspicion is that there is still z-indexing at play here, but we cannot seem to find the solution to it.

Thoughts?