Eeyore is a very cute donkey, best friend of Tigger. He usually loves attention ("Thanks for noticin' me...") and never gives up, no matter how many times the other jerks of Hundred Acre Woods knock it down!
A person that is habitually or chronically depressed, sad, melancholy, gloomy etc., for more days than not. They are over concerned with their problems, no matter how small. They tend to have a round the clock "poor me" attitude. Being around these people has a tendency to "suck the life" out of others.
Man I can't stand to be around bill now days he is a downer! Yeah he really needs to snap out of the "eeyore syndrome" that runs his life.