I can remember getting my first negative feedback. It felt shattering as I put 110% into my ebay store. Luckily I've only had the one.
It's very hard to get negative feedback removed. The only two ways I know of is to have the buyer agree to retract their feedback, or to ask ebay to remove it because it breaks one of there policies.
Unfortunately it's the nature of the beast. At some point you'll get a negative feedback no matter how good the service or how much you try to resolve an issue. Simply power on.