Some baluns are transformers with two windings and electrically isolate the input leads from the output. Other, cheaper baluns are single-wind "autoformers" and will exhibit continuity from input to output even when they are working properly.
Is there any reason to believe that your balun deteriorated? Did it work well, but is now working less well.
Generally, the ones that are 1/2" in diameter are autoformers and the ones that are 3/4" in diameter are dual winding transformers.