BMW K100 RS runs for 30 minutes and dies?

I’m having a problem with my 1987 BMW K100 RS. I got the bike used, but in very good shape and rode it for two years without any major problem. At the end of the season in 2004 while I was riding the bike to its winter home the problem started. I’m going down the interstate at about 80 mph, the bike sputters and stalls, comes back on, and then completely shuts off. I’m now coasting with the stalled engine dropping my speed rather fast. After I made it to the shoulder and stopped I made sure the bike was in neutral and tried to start it. The fuel pump came on and the starter kicked in, but the engine would not start. Long story short, after about 20 minutes the engine decided to turn over and run for about 5 minutes down the road only to occur again.
This spring (2005) I took the bike to the BMW dealer in Ledgewood, NJ to try and find the problem. I left it with BMW in April, and got it back in August; when the dealership went out of business. They had been telling me that it is an electrical problem but were unable to narrow it down. After a bit of testing on my part, for example; ride until it dies, then sit and wait for 30 minutes and try and ride again. I have found that it will run for about 25-35 minutes, seeming irrelevant of miles, before it dies. When you restart it, it runs for a much shorter time maybe 5-10 minutes before stalling.
I know the cooling fan on the bike is not working, but I have also tested that and the fan never tries to turn on and it dies anyway. I also know it is not the major computer components, as these were swapped out with another working bike while it was at BMW and the same problem still occurred.
Does anyone have any idea what could be wrong? I love the bike, and it runs beautifully when it runs at all.