I'm still not sure what button you are referring to. The ExplorerBar has a number of different styles. The only thing I could find that even resembles a menu that closes are the flyouts in the OutlookNavigationPane style. But I don't think there's any way to prevent that from closing since it's essentially a context menu. 

Maybe you can post a screen shot of what you are referring to? 

I did disable close menu last time due to i have no idea to call it back again when user did close it.

Add on information,

the disable closed menu was setup on ultradockmanager1 with set false on ShowCloseButton.

but it will helpfull if there is a function available how to call back the closed explorerbar menus.

The button in your screen shot is a button on a DockManager pane. It's not part of the ExplorerBar. The ExplorerBar doesn't have a close button. 

To disable the close button, you would do something like this: 

var pane = this.ultraDockManager1.PaneFromControl(this.ultraExplorerBar1);
pane.Settings.AllowClose = Infragistics.Win.DefaultableBoolean.False;