I hope that donp is correct. Give it a try.
20Mph is slightly above where the bike should be shifting into second gear. Does the bike shift into second gear properly? If not the jumping forward could be the second gear trying to kick in, and the dieing could be part of the second gear malfunctioning.
Good luck with the gas cap, and repost if that does not help. You could get some other sugestion besides the worse case scenario that I am guessing at.