The warranty from Fitbit is clear that it only covers the original purchaser that was bought from an authorized reseller/sales channel. Pretty much the same language as in most warranties from any vendor.
"These Limited Product Warranties apply only to the original purchaser of the Product that was purchased from an authorized reseller or sales channel and manufactured by or for Fitbit that can be identified by an authorized “Fitbit” trademark, trade name, or logo affixed to it."
Was it broken when you got it? That is on the original seller, so eBay should be able to remediate unless it was purchased "as is". If you bought using PayPal they can step in as well. You can also file an "Item not as described" complaint with eBay.
If it worked when you got it and it failed later, that is a sticky wicket. If it was the latest firmware that broke it then you could discuss that with Fitbit support and they may be able to offer at least a discount on a new product.
