MS201 M-Tronics are renown for failing fuel solenoids. Brad is right to suspect it because that is what the trouble often is. Stihl now has a solenoid valve test routine that should be performed in addition to pulling the data from the module. The fuel trim numbers will tell you what the module is doing to try to keep the motor running properly. The low fuel trim value is typically around 40-45. If you encounter a value down around 30, it tells you that the M-Tronic is cutting back fuel supply (or at least trying to) because it senses the motor is running too rich. Newer modules are "locked" at a minimum high fuel trim of 45. Anything below 45 on high trim is potentially problematic. Stihl has had quality issues with the solenoid valves- there is a new style coming out that is more durable. The M-Tronic diagnostic looks for electrical problems- it will not detect a mechanical problem. Often a mechanical problem will affect the fuel trim numbers and needs to be recognized as such. The new solenoid test looks for pressure leakage that is indicative of a failing solenoid. I don't say "failed" until it fails completely. These "failing" solenoids will leak a little fuel and cause running issues. A leaking solenoid will pass the M-Tronic electrical test, but will fail the new pressure test. If your saw has a solenoid issue, be sure you and your dealer know that the solenoid has a 3 year warranty because it is an emissions device.
M-Tronic is a very dependable engine management system, but it isn't foolproof. A mechanical problem will screw up an M-Tronic saw just like it'll do to a conventional carbureted saw. Has your dealer pulled the data off the module? It won't always tell you what the problem is, but it will help rule-in or rule-out problems. A troublesome tank vent will still cause the saw to die, M-Tronic or not. I'd take a good look at the wires within the handle- the post said that the owner had replaced the handle. The M-Tronic wires are small and delicate- they're easily damaged. I would also recommend putting a Stihl ZAT-4 spark tester on the unit and the M-Tronic testing side cover along with the bar and chain. Go cut with the saw and watch the spark. Does it disappear when the saw begins to die, or does it continue until the engine slows down to the electronic low cutoff RPM? Has anyone checked the fuel filter, fuel hose, and carb inlet screen? Any of these can cause a shutting off issue.
I work on 2 or 3 M-Tronic saws per day and I'm seeing fewer and fewer REAL M-Tronic problems. The new generation of locked modules have solved almost all of the lean running problems. I hope that the new ceramic? solenoid valves are more robust than what's out there right now. I'm an old guy who still uses my trusty 028WB on a weekly basis, but my 3 year old MS261 CMZ is starting to win me over. M-Tronic and other electronic engine management systems are going to be around for the foreseeable future. Adapt or die off. Thats the choice all us old dinosaurs face.