Before replacing the carburetor replace the fuel pipe, fuel line, rubber gas tank grommet and filter. The fuel pipe goes thru the plastic partition that the carb mounts to and a little bit of a PITA to get pulled thru it. The carb inlet "spears" into the grommet and they can start sucking air around it when it rots out or it can split where it goes thr the plastic partition and has the "connector" pushed into it.
They must have had some issue with those saws because you will see several different set-ups and some part numbers superseded when you are looking at the IPL's
I replaced the fuel pipe twice on mine, pretty easy fix once you get your feet wet once with it. Just as a precaution I kitted the carb both times while it was off but neither time were any of the parts inside suspect or obviously defective.
I also had another issues related to fuel where the filter ended up at the top of the tank instead of the bottom and would only run a minute or two after fuel it up before it started having issues. Not exactly sure how that even happened but it was a pretty easy fix, just reached in with a stiff piece of wire with a "U" on the end and pulled it down so it went to the bottom of the tank.
I recently replaced my CS-360T with a CS-355T and never looked back..........Cliff