Mike,

The symptoms you describe suggest an intermittent connection somewhere in
the nav receive RF chain. If the GS and VOR/LOC use the same antenna, and
the GS works OK, this suggests that the problem is most likely in the
splitter or the cabling/connectors between the splitter and the radio. The
"open" VOR output on the splitter MIGHT be a source of the problem, but it's
not very likely. (However, terminations are cheap and simple to install --
I'd put one on just for general principles.)

See if you can duplicate the problem on the ground in an area where a VOR,
VOT, or LOC signal can generally be received. Watch the NAV flag while
wiggling the various cables, connectors, etc. On the other hand, any
avionics shop should have the equipment needed to quickly and accurately
check out the entire antenna/splitter/cabling system.

--
-Elliott Drucker