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Is it a regular multi-process Fly app? I’ve seen similar (but less severe) issues with those once before.
See if these steps give you any hints on what’s going on:
In the meanwhile, to mitigate the downtime, you can deploy the same code to a new Fly application and flip your DNS records to point to those. A caveat, keep this recent shared-IPv4 related change in mind (just in case your Fly app expects dedicated IPv4s): Announcement: Shared Anycast IPv4