If it likes to cut out/die on slopes, that would indicate a layer of water in the carb bowl, it lays in the bottom of the carb
until you hit an incline or hit a bump, and would take some extra cranking to start again to burn off that slurp of water.
When you are trying to check for spark when the battery is low, the engine may not be cranking fast enough to produce
a good spark.
So drop the bowl off of the carb and dump it, it is unfortunate that they don't have a drain plug like on a Honda.
You also might check your valve clearances, they may be on the tight side, making it want to shut down when hot,
and not want to restart until cooled off.
Both of these ideas are free, and not too difficult, and should be a thing you do anyway.