A few more observations:

In Firefox on Ubuntu when I reset the page seems to do a refresh. All the fields including the drop downs go blank for an instant then the page refreshes and shows the top level folders.

In IE it seems to be clearing all the fields, but does not refresh. On IE I click the reset and all the fields clear, and just stay blank.

Is there another script that is suppose to monitor something and refresh when it sees the change? It may be IE is not running that script correctly.

I checked it once more... buttons Submit and Reset have no specified type of button = IE do not refresh page and any other browser refresh page

So you can try to modify buttons this way:
components/com_joomdoc/views/documents/tmpl/default.php - around line 92
<button type="submit" onclick="return JoomDOC.searchSubmit()">' . JText::_('JOOMDOC_SEARCH_SUBMIT') . '</button>
<button type="submit" onclick="JoomDOC.resetSubmit()">' . JText::_('JOOMDOC_SEARCH_RESET') . '</button>

Good news! Adding the type="submit" to the reset button works! I didn't modify the Submit since it was already working. The search now resets correctly in IE.

Thank you!

Chris