Could be pump or filter....or many other things...
Good job on letting the bike warm up...seems like no one does that anymore, I let mine warm up for 5 min +. "Stops shortly after," I assume it stalls then? I don't think dust and mud would effect the internal filter, but take a look at it anyway. To get it started after a stall it often helps to turn the key on off again to prime it.
This just all of a sudden happened? What kind of mods do you have? Did you maybe pump some bad gas? Interesting issue, more details please!