Apparently, Roscoe Scully recorded a version of How come my dog don't bark when you come round for Crest records in the 50s or early 60s, Lewie Wickham recorded it in about 1970, and Buck Owens recorded it in 1977. I checked the Library of Congress SONIC catalog, among other things...

There's also How Come My Dog Don't Growl at You?, copyrighted by Charlie Williams in 1960 and recorded by Sweetpea Johnson in 1961. I don't have lyrics for that one, but we're obviously dealing with a recurring theme in blues, country and rock...