I have implemented a bit of a change to the DropTree Field Type that will make the popup div stay in place if the user clicks on part of the empty part of the div and not an item from the content tree. Essentially, if I click on any of the empty white part of the div below, and not e.g. “Sample Workflow” then I want the drop tree to remain open for me.

First of all you will want to open the Sitecore.js file that lives in you webroot under …..\WebSite\sitecore\shell\Controls\Sitecore.js.
Open this file an make the following changes:
1. Add a variable up the top of the file called BlankDivCheck like so
this. BlankDivCheck = null;
2. Search for the line scSitecore.prototype.postEvent = function(tag, evt, parameters): and append the following code after the following line of code “var ctl = this.getEventControl(evt, tag);”
BlankDivCheck = false;
if (ctl.className.toString() == “scTreeItem”) BlankDivCheck = true;
3. Search for the line scRequest.prototype.resume = function(), and change the following code
if (this.closePopups && typeof(scForm) != “undefined”)
{
scForm.browser.closePopups(“Request”);
}
To this code:
if (this.closePopups && typeof(scForm) != “undefined” && BlankDivCheck!= true)
{
scForm.browser.closePopups(“Request”);
}
4. Save the file and go back to your Sitecore Desktop or Content Editor. You will want to refresh the cache (Ctrl + F5) as well as deleting all temporary internet files from Tools-> Options -> General Tab -> Browsing History -> Delete Button -> Delete All. Once this is done, refresh the browser and go check out e.g. the Workflow Field Section of an item as discover that when you miss clicking on an item from the content
tree, the div stay open.
Enjoy.