Not having a lot of additional info as how long does the saw idle prior to actual cutting etc. or how long you cut prior to letting off the throttle and the saw stalling out . I would think that perhaps the saw idles fine when cold (fast idle) then once warmed up it has a over rich carb setting causing the stalling issue. Have you checked you plug recently . If almost new then the plug should have very little discolouration . Give it a check it should be light brown colour if dark brown or black then the saw is running rich and the carb will have to be reset . Let us know what you find . A secondary issue could be within the air cleaner element , but I will await your response .

Thanks for your reply. I'm sure I didn't let it idle long enough. Maybe a couple minutes.

Are you talking about the spark plug or some other plug that I should check?

Spark plug is what I was referring to . Also once you have checked it ensure all fuel line connections are tight along with the carb flange bolts . You said that the air filter is not restricted with debris correct . Also since your at it the fuel filter should be inspected. Ensure that you can blow air through it . After that carb inspection and cleaning and tuning would be next . Check the 1st three scenerios1st and report back .

I was able to fiddle with this tonight. The spark plug is definitely dark brown. Almost black. I let it idle for about 10 minutes. The chain wasn't moving when it started and after about 7 minutes the chain started spinning quickly and flinging oil all over the place. I assumed it was warmed up after that point so I tried the throttle and it revved up fine but still died after I let off the trigger. It didn't die as quickly this time... more like sputtered out instead of instant.

The air filter is clean as a whistle but I wasn't sure where the fuel filter is. I checked the manual and the blasted thing doesn't have an exploded view. I will have to see if I can find that online.

After inspecting it more I noticed the carburetor adjustment screws take a special tool. These guys really don't want you fixing this yourself because it's also surrounded by a plastic shield so you cant just turn them with pliers or something. The tool looks to be about $50 online. That really burns me up.

Thanks so much for the help. This has been a real learning experience so far.

Ok sounds like a unit that has sat and not been used for a while . Ensure you have fresh fuel . Just a little tender loving care is all that needed . I would get a new plug , you can clean and keep the current plug for a spare. The carb High and low speed jets can be dremeled to accept a slotted screw driver later . If not you should be able to find the proper adjustment tool cheaper than fifty bucks on ebay or Kjiji . I have them all since I repair saws routinely. Find a quality carb cleaner solution. I use to use Lucas top end cleaner , but Startron available at Napa is a great carb cleaning agent . One ounce mixed with you premix is all that is needed. The fuel filter will be within the fuel tank at the end of the fuel line . Use a piece of wire to fish it out or long nose needle nose pliers. I personally do not admire Poulan saws , but that's another story lol . One other point is to ensure your choke setting is set properly , you can verify buy checking the carb venture when time permits . Yeah you running very rich by the plug dark colouration most likely . When you make your next fuel mix go with a premium 2 stroke oil and run it at 50:1 ratio. I prefer Amsoil but any premium grade such as Echo or Stihl will suffice . Keep us posted . Good Luck !