Locking the Open File Tabs bar is not possible. But I think you mean "docking". If your Open File Tabs bar is currently floating and is therefore a small window with a title bar which shows Open Files then simply double click with primary (normally left) mouse button on this title bar to dock the bar again. It is possible to dock the Open File Tabs bar also at bottom of the UltraEdit main window.
Once it is docked again where you like it, move the mouse pointer over a free area of the bar (not a file tab and not the small x for closing the bar) and press the secondary (normally right) mouse button. You will see a popup menu with only 1 item: Undocking allowed which is currently checked. Click on this item with primary (left) mouse button to uncheck it. Now it is not possible anymore to undock the Open File Tabs bar by mistake with a double click over a free area of the bar instead of an open file tab to close the file which I think is what happend.