some of those blower carbs don't last that many years. There is a small flap that is part of the gasket that acts as a valve when fuel is delivered - when the flap fails fuel doesn't get pumped to the carb and the mixture goes lean. It is just as expensive to buy a whole new carb as it is a repair kit. I think the last couple cost me about $15 on E-bay. Zama carb is what mine takes - same model on the little mantis tiller, leaf blower, weed wacker, leaf edger etc. It sounds like that might be what is happening on yours. Zama makes a couple different carbs so look at the manual to see which it is.
Basically the above is correct, the price of replacements is so low it is not economic to try & fix most of them.
You really need to go to the makers web site .
The major makers , Zama, Walbro, Tillotsen all have repair manuals on line , although it does require so digging to find most of them.
Because tollerances are so fine on them, I never ever reuse old gaskets & diaphragms.
Compressed air, unless it is a spray can is a big no, no on them because it will blow dirt particles so hard into some of the passages it can never be removed.
All of the jet holes are tapered so should be blown out backwards.
There is a methodology to fixing hand held engines and it is fairly important.
A partially blocked exhaust will cause the exact same symptoms you are describing and is by far the second most common fault that comes into the workshop.
The most common is dried up fuel, just so you know.
Joe Pace did a really good set of videos on U tube called two stroke diagnosis.
Unfortunately he never finished all of them but well worth a visit.