I'm guessing the binary they use from Apple (IMDAppleServices) to generate part of the registration information probably adds metadata to the "validation blob" that gets sent to apple when registering beeper mini as an iMessage device.

If the metadata includes the OS version, Apple probably blacklisted any new devices registered in the past few days with validation blobs generated from that binary.

(The binary was sourced from OS X 10.8 which is ~11 years old now)