Having an un-terminated connector on the splitter will not cause the
problem you are describing. Definately trace out the coax from the splitter
back to the antenna and look for splices (connectors). A poorly made
connector could add a lot more than 1db of loss. Look at the antenna
connections and balun... it could be the orginal (how old is your airplane?)

Don't overlook the possibility that the radio is not seated all the
way in the tray.