I have 2 Stihl saws and both had minor problems. One's chain saw nut was loose and the chain saw end just fell off while cutting. The other gave me a hard time starting this winter but it was more me than the saw.
In both cases my local Stihl dealer gave me free advise and even a free nut.
It would be easier if you gave us a model# but here's some general recommendations. I think points 3 and 6 will solve your problem.
1. Set the chain saw for winter operation. Each saw is setup differently but check your product manual to see how this is done. What this does is prevents carburetor icing.
2. Check your air filter and clean it out if necessary. A dirty air filter could cause the engine to shut down at lower speeds.
3. Check your spark plug. It sounds like it might be dirty or the gap is bad.
4. Check the oil/gas mix. If it is old, then mix thoroughly before using or discard (in an environmentally correct way of course!) OR start a new mix.
5. If you have a spark arrestor in the muffler (unlikely), clean it out.
6. Check out the high speed, low speed and idle speed adjustment screws on your chain saw's carburetor. Check your product manual to see how to adjust them. Most likely you will need to adjust just the idle and/or low speed screws.
Hope this helps!