This guy not only had a soon-to-be-famous shikona, he also had 18 consecutive losses in jonidan, after a 7-0 no less. Talk about the perils of overpromotion...Not sure he's the worst, but given that the most losses you can have without two 0-7's is 19 (6+7+6), he's a pretty good bet, at least for the period of time for which the DB has hoshitori available (last ~50 years).
I don't know if this is the record or not, but Futatsuryu had 21 consecutive losses in makuuchi/juryo.