I've only been with them through one major incident so far, and I recall them handling it reasonably well.

You can see them responding to customers and providing updates in real time here: https://community.fly.io/t/there-seems-to-be-an-outage-with-...

And a detailed postmortem here: https://community.fly.io/t/major-outage-portmortem-2021-10-1...

They also update their status page pretty diligently whenever something goes wrong even for things that don't necessarily impact all customers (the only recent item on there that affected my app directly was the Oct 13 one from what I can remember): https://status.flyio.net/history