If it had a universal gas filter added in between the carb and fuel pump (assuming it has a mechanical pump on the engine,not an in-tank electric one),make sure the original paper or brass filter that is in the carb under the fuel line nut is removed,because having both can restrict fuel flow enough to cause issues on heavy acceleration or long uphill grades..
Some of those in the carb gas filters have a "roll over valve",a check valve that supposedly wont let gas drain from the carb if the vehicke rolls over..

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Those can be troublesome sometimes--I either tossed those filters away and used a universal in-line clear type one,or put in the older style filter without that rubber check valve..
The oem filters suck,once they plug up,the spring behind them allows the fuel to push it out of the way and let dirty gas by-pass it completely..not a very good design..
Also look and make sure no one added a filter between the gas tank and fuel pump--having one on the suction side is usually no problem,but might cause enough restriction to starve a carb on an engine that guzzles fuel,especially under the conditions listed above..
The sock filter in the gas tank on the sending unit is very fine mesh,and water cant pass thru it easily,nor can any silty rust--it may build up around it due to the suction of the fuel pump after several minutes and eventually starve the carb for fuel..
Water in the gas can usually be eliminated with some dry-gas additive,as for rust,the best fix is to pull the tank out and flush it good (or replace it)--I have gotten around this issue on a few vehicles by putting a strong magnet on the bottom of the gas tank (like one off an old junk speaker,or hard drive)--place it near a corner,away from the sock filter ,so the rust it'll attract will be kept away from the fuel pick up tube and sock in the tank..
I had one truck I bought that sat with an empty gas tank for years--it clogged up several universal fuel filters with rust in a short distance--after I had replaced them about 5 times,an older mechanic told me about the magnet trick--after I added one,I didn't have to change it again for over a year,and it didn't look like much rust was in it,I just did it for peace of mind..
The tank not being vented could cause this as noted also..also any old or original rubber fuel lines wont be ethanol compatible,and can come apart inside and cause a blockage intermittently--best to replace all the rubber fuel hoses with newer stuff rated for ethanol--I see this on many riding mowers that have the same issue--runs great for a few minutes,then "runs out of gas",even with a full tank..old hoses can crack and be a fire hazard once ethanol eats away at them long enough too..