Sounds like the fuel system is the problem. Your year HD have had problems with the fuel lines inside the fuel tank cracking resulting in the fuel system sucking air. Some of the symptoms of this is the bike running rough, poor idle, popping, backfiring and stalling to mention a few.
Fill the fuel tank and see if the bike runs better for a while and then the problems return after the fuel level drops, this would be a sign of cracked fuel lines.
You may just need to change out the fuel filter, when was the last time this was done.
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08 FLTR candy red sunglo,with 2015 103 HO, V&H Dresser Duals with Monster Rounds, Power Vision tuner, Willy Shiny Wheels and Forks and a bunch of other stuff.