From what I've seen the most likely culprit would be some type of chemical poisoning. Since you only had him for a couple of months and he stopped eating only a week ago I would rule out some other common culprits like thiaminese poisoning which is actually a nutritional defiencency, this takes more time. Disease like internal parasites wouldn't kill so fast after stopping eating. While not impossible but very unlikely a protazoan disease like ick, eels are very resistant and only the very sickly usually succumb to a protazoan disease.
SO the big question, does your lfs run copper in their system, or did you treat with copper or run it in your system. Did you use any tank cleaners or pest eradicators; like vibrant, chemiclean, flatworm exit, etc. Cyanide is also used more frequently but many times the body would be washed out, seizures usually accompany cyanide.
If it's not your tank then it falls to disease, nutrition, or chemical.