Bottom line is that you are relying upon someone with very little vested interest in your company to represent you. Some drop shippers do a far better job with these than others. It pays to do some research.
1) Presentation of the package. Will the item arrive nicely packaged to delight the buyer? Or will the buyer be shocked at the package when they first see it. How the item is packaged is your LAST chance to leave an impression on your buyer. It's the buyer's final experience with you and can mean he difference between good ratings and bad ones. Trust me, customers do not care if an order simply arrives despite the packaging. They want well packaged items. My story is not from drop shipping, but my only eBay neutral rating was from a buyer who rightfully said that I didn't do a good job packaging an item and it was lucky to get there. He was right. I got in a hurry, forgot something and tried to open the package, put the missing part in, and closed it with tape. Looked terrible and I got a deserved neutral rating for it.
2) You often cannot keep a real time count of the drop shippers remaining inventory of items. SOME drop shippers say you can. MOST of them say any inventory feed you get is not guaranteed to be up-to-date. That disclaimer doesn't satisfy a paying customer when you cancel an order due to lack of inventory.
3) Upward price changes after listing an item. Once an auction gets a bid or an item reaches a certain point, any change in your price may not be able to get into your listing price and you are stuck selling it for less than you assumed or ending your listing early. It's easier to know your costs when it's sitting at your location.
4) Slow tracking information. I know one seller who lost his top-rated seller status because his dropshipper wasn't providing the tracking information in time to satisfy eBay's metrics.
5) You have no idea what your drop shipper shipped nor do you get to inspect the condition before it ships. So buyer says the item arrived looking dirty or used. Maybe it did, maybe it didn't but you don't know because YOU didn't package it. But YOU are stuck in the middle because you sold it.
Don't hear this wrong because there are some people and drop shippers that can work very well together. I've used a couple of them with good success and no negative feedback. But it takes work to stay on top of these issues.