I wouldn't call it "solid theoretical footing". The rough sketch of QKD is

1. BB84 key exchange requires an authenticated channel. typically you do this with a 2. Carter-Wegman MAC, which is information-theoretically secure, but requires shared randomness that cannot be reused.

Successful protocol execution refreshes randomness (you can net gain from it), so you can communicate back and forth continuously when everything is working. An MiTM who simulates a network failure though can expend some of your pre-shared randomness (without it being refreshed). If they do this enough, they can exhaust your shared randomness, and bring down the link until you exchange more shared randomness somehow out of band. if you want to maintain information theoretic security, this might involve e.g. a courier with a USB or whatever (or a carrier pigeon, who knows).

This is still "secure", but is also a significant issue any QKD (even "real" QKD) has that classical cryptography does not have, and has always made me question the "solid" story for QKD.