If you mean pushing the key in to choke…it’s likely you might not be doing anything there…if she’s an efi. Anyway…
Things I’d check, if she was my own…
I’d quickly check the voltage measured at the battery, just before and up to she starts to run poorly or not at all, when lower in the rpms. Rule out any insufficient charging reasons out of play. At the same time…rule out a compromised stator, regulator and battery too (a small engine like this is easily turned over by even a poor battery, but only a decent battery will be man enough to run ignition, fuel and sensory items sustainably..especially at lower rpm)
Then, armed with a fuel pressure gauge (of your choice…obtainable for not far off $10-20 online), check the fuel pressure in and up to the aforementioned state of running.
I’d then check the voltage and position set up of the tps (if she is efi). Check the throttle body operating too.
Measure the continuity of the coil packs and leads.
Check (probably should have came further up the list in order) if you have a fuel rail filter screen. Good chance you might. Certainly from around then onwards, they usually do.
Good to determine (if we are thinking it’s a fuel issue) and prove the presence of fuel delivery at given locations along the delivery route. So assuming the fuel tank primer bulb is in good shape and fitted in the correct direction of flow, the tank and engine fittings are in shape (not drawing air, especially if it’s the newer plastic quick connect type)..then the presence of adequate fuel pressure at the test point on the rail…and the rail fuel screen is clear…all that’s left is an injector issue. This is usually quickly indicated, by the sensory told presence of fuel in the oil. Smell and sight. Often even indicated by a higher than normal oil level on the dipstick.
Finally…failing all that…back to electrical and sensory items. In brief..if you are getting a decent voltage indication and sustaining…it’s odds on to be a fuel related thing. Start simple, at the tank and delivery then work up towards vst and the usual seal perish issues within.
Voltage, electrical integrity (including terminals and earthing) and fuel.