I had this happen last week.

DL repeatedly showed $Y as the price during the search and booking process, then at check-out, it said "This fare is no longer available. The new fare is $1.4Y."

I searched repeatedly over a 90 minute window, using different computers, browsers, and networks (VPN, public, home, etc.). The entire time, the search results displayed the same price, but the check-out price fluctuated $100 each way of 40% above the search result price.

I got fed-up and called in. The agent did the same search on her computer as I did at the same time on mine. She could see the search results I was getting, but she got different check-out prices than I did.

After multiple attempts, she told me to book the routing and best fare I could find that would allow for a check-out. I did this, but the times of the flights were 6-hours off from my desired plans.

Once I did that, she found my reservation changed my trip to the originally desired flights and forced the price change to zero for the correct flights.

She apologized for the confusion and said she couldn't explain "why the system does that". She saved me a ton of money and I couldn't have been more appreciative.