I noticed your model listing states 5520c do you have any lights on in the bottom right hand corner of you meter assembly of your dash?
What rpms are you idling at?
Can you hear the engagement of the fuel feed pump with the key in power position( should be hearing a repeating clicking sound coming from right hand side of engine near fuel and oil filter)?
Did this abruptly start or has this been occurring on and off and become more noticeable over time?
will the tractor run at any rpms above idle?
the fact you using your bucket is drawing down the engine enough you lose a good portion or you rpms is also slightly concerning, but this probably directly related to the running issue, to me it almost sounds as though its not getting proper fuel flow, or the fuel system is becoming restricted, i would start by checking the fuel lines to make sure none of them are crimping themselves, or folding back on themselves, i have had new units come from the factory, and fairly new units that were purchased, with the fuel lines a bit longer than they should be and the way they were routed caused them to crimp them selves into a closed position while in operation and basically starve themselves till they die, if those all check out then i would move on to checking the condition of my fuel filter to make sure its not plugged up with trash or water, then we would check the feed pump, and fuel stop solenoid to make sure they are operating, then finally if that all checks out we would move to checking the rest of the fuel system.
but I'm thinking your failure point is most likely going to be the fuel feed pump, i say this because the fuel injection pumps for the 20 series models, generally have enough suction power with the main injection pump to pull enough fuel to themselves to start and run for a bit but the more rpm's you try to give it the less its capable of keeping itself feed with the proper amount of fuel causing it to lose power(rpm's) and then die, branson/tym uses this fuel feed pump( usually 4-7pis) to keep the fuel flow at a constant rate to the fuel injectors, if there isn't a constant flow it can do exactly what your describing.
hopefully all this info helps you narrow down your failure and get it resolved and you back up and running
