Hey guys, been prowling these forums for a while now (bought my savage a few months ago thinking of it as a starter bike, you all are doing a fine job of changing my mind...) but I'm now compelled to jump in and finally post.
I've been having this exact same problem, only the bike doesn't restart on its own, even when I switch it to prime - I have to pushstart the bike to get the engine to turn again.
After reading about the petcock, I hopped on ebay and found one in perfect condition from a salvaged '99. I haven't had the problem in about 2 weeks, so I put off popping it in this past weekend as I had planned.
Lo and behold, it cuts out again today, this time pretty suddenly and in the middle of the leaving-campus rush. I pulled off the road, cursing because I knew I was gonna miss the movie I was headed to, and immediately pulled the vacuum line to see if there was gas in it - completely dry. I pulled the fuel line and the petcock functioned as it should - flowed in prime, but not in on.
My bike is a totally stock '01. The only modification I've done was to swap the old fuel line for some 5/16" fuel line because the old one was cracking at the end. I've changed the oil once with standard Castrol 10w-40 synthetic. I took off the tank to replace the spark plug last week before realizing I had no idea what I was doing (the manual described using some kind of spacing gauge..
.). Also, I figured out with the help of these forums that I have the dreaded (or at least very irritating) plug/cap oil leak.