By all means, don't drop him, especially if your league has holds as one of the scoring catagories. Eddie will continue to pitch for someone, somewhere. Continue shopping him around, you may get lucky! I'd keep an eye on the situation and start reading up on the Mariner bullpen to see if anyone would have an inside track to the closing job.
Here's a name to keep in mind...Rafael Soriano. I went out on a limb and picked him up.
But don't take my word as gospel, I'm in seventh place!