On September 29, 1996 I saw a comet-like object near Jupiter. The next night it was gone. What was it?

Jupiter was at RA = 18h 38m 29.7s and Dec = -23d 21' 55.6" and the globular cluster Messier 22 was only 1/2 degree south at 18h 36m 24s and -23d 54'. I think your comet was this bright globular cluster which is almost as big as the Full Moon. As to why you could not see it later on, Jupiter moves about 2 degrees a night or so, so you would not have seen M22 near Jupiter in subsequent nights unless you really looked far afield.