Everyone so far has given you excellent advice, and from my experience, they all work. You probably have a rough chamber, or you haven't cleaned it "enough", or both. I've had a Colt that would not eject and would literally punch a hole in my hand with the ejector rod after only 12 rounds. I also have lots of S&W's that can shoot 500+ rds in one day and will eject everytime (When I was younger, I could shoot more, but "arthuritis" as my grandma used to say is the limiting factor now).
The cheapest alternative and first choice I would undertake is to buy a "chamber" brush for a 357, or a .40/10mm or .45 bore brush, and put them in a battery-powered hand drill and go slow with Hoppes or my choice which is "Ed's Red" (recipes everywhere). Hoppes does smell better.
Brownells and Midway sell the chamber polishing supplies, but unless you have experience I would shy away from that option.
If you have a nice local gunsmith, he should have a chamber polishing setup, watch him do it (when I was a kid my neighbor was a gunsmith and I spent lots of time with him in his hobby garage), and pay him the fee which shouldn't be too bad. You can later buy your own equipment.
I would go with this option if it is cheaper than shipping it to S&W - but I would insist S&W pay the postage both ways.
Good Luck.