I've had revolvers that did the same thing. But they weren't Taurus. One was a Ruger, the other a Colt.
I'd give it a good cleaning. Someone else has mentioned cleaning under the ejector star. Someone else mentioned the forcing cone. Clean those well, especially the forcing cone. I've seen a build up of bullet lube and lead that would cause the cylinder to bind there. Clean the front to the cylinder well too. The Colt I mentioned, I had to take a brass brush (lightly) to the forcing cone area to get the crud off it. Never had a bit of trouble with it again.
Flush the internals with gunscrubber, and give it a few drops of oil. Put a drop or two on the ejector rod and hopefully, you'll be good to go.
I had one of those Taurus 38's back in the day. I forget the Model number, but it was an 80, 82...something like that. Fixed sight, more or less Model 10 copy. Good shooting gun, but man that thing had some UGLY grips.