Unfortunately, this exact thing happened to me during the post-Christmas sales in late December 2017 and early January of this year (2018). It was the Dooney.com website (I've never had a problem with ILoveDooney).
Dooney handled it really badly. This should be basic: the website should not allow people to check out and pay if all of the stock of an item has already been spoken for through other orders, whether or not those other orders have been fully processed and shipped out. Plenty of other websites automatically show the customer an "Out of Stock" notice when the customer attempts to purchase and pay for an out of stock item. Their computers have no trouble keeping up with what amount of stock has already been ordered and what, if any, is available. I can't explain why Dooney's site cannot keep up enough to offer us the same Out of Stock sign instead of allowing us to purchase an item that may not exist.
It took me such effort and time--5 or 6 LONG phone calls over the course of January into February--to get everything put to right. By that I don't mean I got the item in question (that bag materialized for a few hours around two months later on the site, only to disappear again for the rest of the year). Rather, my hard effort resulted in what I suppose is the best Dooney could muster: a refund, at LONG last, of the money on my debit card (I'll never use debit card with them again) and a 20% discount code for any bag on their site.
I didn't order from them for most of 2018 because of that.
Eventually I started ordering direct from them again because I just like their bags so much and the main Dooney site has some exclusive designs that don't get sold anywhere else, even I Love Dooney.
Here's hoping your situation doesn't turn out like mine.
Thanks for the reply! It helped to decide how to proceed with next steps. After calling twice on Saturday, once on Sunday, and twice on Monday, I finally gave up and cancelled the order. Unfortunately, no one in the fulfillment department ever replied to the customer service rep who tried to help me, and their database system kept showing my item as "scheduled to be released." However, my view of the order details online continued to state, "Backordered." Hopefully, the hold on my credit card will release in two weeks. If not, another callback will be made. On Monday morning (12/17), I tried speaking to a supervisor only to be told she would call me back. After not getting a callback by end of day, I asked to leave voicemail for a supervisor (she was in a conference meeting), only to listen to her voicemail message and get the notification "...cannot leave message, mailbox full." It's an unfortunate set of circumstances to quickly lose a potential loyal customer. Moreover, their San Francisco Premium Outlet location had one in stock and on sale for $219 the same day I placed my order online, and for $20 in fare (also 4 hours round trip) on public transportation plus $20 more for the handbag, I could have purchased it. Sadly, it was just two opportunities lost from that sales day. I must say, I am highly impressed with the quality of Dooney & Bourke handbags, as I have purchased a few from QVC.com over the past three months (Florentine Brenna Satchel and Embossed Croco Deana Satchels). I bought a City Large Barlow in Black on December 3rd from the Dooney.com site and it shipped out the same day. I guess my expectations for quick delivery service based on my prior purchase was a one off. I'm very happy with the handbags I have purchased from QVC - love those EasyPays - and I'm happy with my City Large Barlow. I will no longer order from Dooney.com and will most likely not make any future Dooney & Bourke handbag purchases. Again, thank you.