This will be a simple overview about getting negative feedback removed if possible. First I would recommend reading my article about returns because that's usually where negatives come from.
First, I want to explain some things about my personal eBay Test Store. I have around 5k transactions within 1 year of opening the store. I raised my margins extremely high around month 6, if you want you can read about advanced profit margins here. I have had hundreds of returns and I have had 3 negative feedbacks ever. All 3 have been removed. I have 100% feedback on 2200 total feedbacks given. On my last negative, I was still showing 100% because they round up the 99.9 to 100.
Now, I want you to know that my customer service is very good. I always really do try to help my buyers out. I have lost money on sales due to repricing timing, or order errors. Here's an article on reasons for that.
My customer service has helped out with most of my feedback. Being honest helps; people have asked me why they received an item in an Amazon box. I tell them that the vendor for that brand ships from their Amazon fulfillment. That person left me a positive right after I explained that.
Use the eBay Feedback Revision
To try and get a feedback fixed in the beginning is to try to resolve it with your buyer. Just ask if there's anything you can do to make the transaction a good experience. If they give you some opportunity to resolve it and you fulfill that request, you can open a feedback revision request; little tip on these, you get 5 to begin with, and you get 5 additional per 1,000 feedbacks given to you.
Use eBay's Policies in your favor
The other side of my way to prevent potential negative feedbacks is to use eBay's policies in my favor. If a buyer opens a return, and I accept it and provide the correct return label, and the buyer doesn't ship it back within 5 business days, eBay will simply close the return in my favor and now they can't leave feedback.
Sometimes you can ask the buyer to open an item not received case, if you can prove delivery you can show that to eBay and they'll close it for you in your favor.
Other times a buyer might leave feedback that is absolutely false, like if they say you shipped it late, or that you never responded to them and you can prove to eBay otherwise. Basically anything that can be proven untrue you can get removed from my experience and from what eBay reps have told me.
Mostly though, using our software, you'll get great results even if you don't have great customer service. Your feedback will suffer but I wouldn't expect it to ever be below 99% unless you are very new and you have less than a few hundred feedback.
If you call eBay and they won't remove the feedback and it truly is an unreasonable negative feedback, you can call back and talk to another agent. Ebay calls this agent fishing and they don't like it so just beware of that I guess.
If a buyer sends you a message that says anything remotely close to threatening feedback for services, eBay will remove the negative feedback if they end up leaving it.
Example: Hi, you sent me this but it was missing some parts... I just wanted to let you know that before I left you a review.
You can call eBay and show them this message if the buyer leaves a negative and they'll remove it for feedback manipulation.