Without data to back me up, I am still positive that no group has preached "Armageddon-Soon, any-minute-now" longer than the group that became known as Jehovah's Witnesses.
With 130 years under their belt, they gotta be the champs. Oh, there have been groups that knew the end was coming eventually, but they weren't preaching it like the JW's were. There were groups more sure of their doomsday, but the groups are gone or their campaign has ended.
JW's are the champs.