In professional Japanese sumo the wrestlers - sumotori - are divided into ranks, depending on their skills. In the top division (the makuuchi) are the maegashira, and in the top part of the makuuchi, called sanyaku, we find the komusubi, the sekiwake, and the ozeki. On top of that sit the yokozuna, by many definitions not really part of sanyaku.
A "sekizeki" is an ozeki who repeatedly teeters on the verge of demotion. An ozeki may, unlike other sumotori, suffer a poor result in one basho (tournament) without losing his rank, but then he needs to shape up - or get demoted to sekiwake. If he does indeed shape up he is safe for another basho, and so on.
Ozeki who keep balancing along this line are, jokingly (and probably not to their faces) called "sekizeki".
My source for this one is, besides hours upon hours of watching sumo: Sumoforum's wonderful Glossary.