I'm having the exact same problem with my '98 Sprint Sport. If the petcock is on "run" or "reserve" it runs fine for a couple of miles then dies. put it on prime and she runs like a champ. I took the bike apart (tank off etc) and found that both fuel feed lines and the vacuum line all have splits in them. I think (hope) this is causing the petcock to stay closed which starves the engine of fuel. I put a new battery in it yesterday, and I have ordered new fuel feeds and vacuum lines from the dealer (for the handsome sum of $75)...I have my fingers crossed that they fix the issue. I've been reading some other posts talking about coils and igniters etc which are scaring me a little.
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