This just happened to me, twice.
On Wednesday the 17th (several days before Father's Day weekend), I placed an order with one-day shipping to make sure my gift would arrive in time. By Friday, some of the order had come in, but the gift was still missing. I called Amazon, and they said the package was lost. They advised me to place a new order with Saturday delivery and they would refund the difference.
Sure enough, Saturday evening rolls around and still nothing. Neither package ever came. When I called, they said it must be lost (again?!) and they would just issue a refund. The gift was a $150 item, so I had over $300 worth of charges on my card that I would have to wait for refunds on. Both items were Prime-eligible.
When I complained, they said they would give me a free month of Prime. Um, no thanks. You tied up my funds, screwed up my holiday, and kept me on the phone for a combined total of 2.5 hours from the three times I had to call to figure out what the hell was going on.
I wrote to the CEO (Jeff Bezos) on the odd chance that I'll hear something back. I understand this isn't directly Amazon's fault, but in the end, they're the ones responsible for making sure their customers actually receive the items they buy. If they had been more willing to work with me (you know, placing the re-order themselves instead of making me tie up my funds) or perhaps offered me a gift card or something, I wouldn't be as pissed.