Do you have the main mIRC Window set to Always "On Top"? Right-click mIRC's titlebar or application icon and inspect the "On Top" menu selection checkmark.
Do you have "desktop windows" set to semi-transparent under Display > Options > [Windows...] > "Transparency for desktop windows:" [n%]
Interface awareness: The log viewer window does not inherit mIRC main window's Always On Top setting and will have to be set to On Top itself otherwise it may be trapped beneath the mIRC main window. Play around with the settings under Display > Options.
You can also try this alias to fix layer transparency for a given desktop window. Add the following alias by typing:
/alias F9 setlayer 127 @ $+ $activewid
/alias F10 setlayer 255 @ $+ $activewid
Then hit the F10 key while viewing the Log Viewer. (Hitting F9 should make the active desktop window semi-transparent again.)