We present Prognosis, a framework offering automated closed-box learning and analysis of models of network protocol implementations. Prognosis can learn models that vary in abstraction level from simple deterministic automata to models containing data operations, such as register updates, and can be used to unlock a variety of analysis techniques -- model checking temporal properties, computing differences between models of two implementations of the same protocol, or improving testing via model-based test generation. Prognosis is modular and easily adaptable to different protocols (e.g. TCP and QUIC) and their implementations. We use Prognosis to learn models of (parts of) three QUIC implementations -- Quiche (Cloudflare), Google QUIC, and Facebook mvfst -- and use these models to analyse the differences between the various implementations. Our analysis provides insights into different design choices and uncovers potential bugs. Concretely, we have found critical bugs in multiple QUIC implementations, which have been acknowledged by the developers.