1. Low Profits
   When using drop shipping you are not getting any wholesale quantity discounts.  None.  So, you pay the highest possible price.  This, in the real world, is called retail price.  However, since it will be below the MSRP (Manufacturers Suggested Retail Price) it is still considered a wholesale or discount price.  But it is not a price that will allow you to compete on eBay.
    
2. Inventory Nightmares
   When you use a dropshipper you are at their mercy in terms of inventory.  Something may be available when you list it for sale but once you sell it on eBay and then go to your drop ship supplier to buy it -- it is gone.  This can cause you to get terrible feedback, have to make refunds, and put your eBay store out of business.  This happens all the time.
    
3. Scam Swarm
   It is nearly impossible to find a reputable dropship company online.  You will end up paying money for worthless dropshipping or wholesale lists and get nowhere fast.  Never buy one of these lists unless you understand what you are getting.  It will be some urls to wholesalers & dropshippers who may or may not be legit.  There are SO MANY fake drop shipping companies out there it is hard to see through all the smoke.  Chances are you will run into a dozen "scam" drop ship sources before you run into one real one.

I would never recommend drop shipping.  It does not work on eBay.  For some real good information go to Google and search for "drop shipping sucks" and you will see how people really feel about drop shipping.

Good luck -- and remember, all drop shipping sounds too good to be true.  And it IS (on eBay).