I think that part of the problem with Koch is that Jerry Manuel is way too trigger happy with closers. Koch is the type of pitcher that needs to get into a groove, and can then become virtually unstoppable. This early in the season, he should have just stuck with his closer until he completely proves incapable of doing the job, because it's not like Koch doesn't have a track record of being an upper tier closer. Manuel did the same thing last year, going way overboard in demoting Foulke and then watching him go to Oakland and tearing things up. Also, compare how Manuel has handled Koch to how Art Howe has handled Armando Benitez. Benitez got off to a start almost as bad as Koch's but Howe kept sending him out there and he has been finding his groove lately, successfully saving his last 7 save chances.
Even if Manuel does make Marte his closer and demotes Koch, as soon as he is fired, which probably won't be much longer, the new manager will most likely give Koch another shot. The problem is just that Manuel has proven to be completely incapable of managing closers properly.