The earlier posts have covered the most likely causes.

1. Ejector rod loose, backed out enough to interfere with the detent pin where the front of the rod locks into place under the barrel.
2. Debris build up under the ejector star at the rear of the cylinder, interfering with engagement of the cylinder lock.
3. Function of the cylinder lock (left side of frame behind cylinder, thumb piece connects to a sliding bar under spring pressure to operate the cylinder locking mechanism at the rear of the cylinder). Should operate freely and have good spring tension.

Beyond these more obvious things I would start thinking about improper assembly or damaged parts (bent ejector rod, broken or jammed spring at front or rear latches, cylinder crane bent).

It is becoming more difficult to find gunsmiths (in general) and those familiar with revolver mechanisms (in particular). If you are not comfortable with doing the disassembly and examination yourself it might be a good idea to ask around at FFL dealers in your area for recommendations. There are a few older gunsmiths, perhaps retired and doing a little referral work out of their homes. For an experienced gunsmith the problem should be identified in a few minutes time.

I have a small supply of vintage S&W K-frame parts (springs, pins, internals, hammers, triggers), if you find that yours needs something send me a PM and I'll try to help.