Every single mobile network will maintain IP addresses when migrating between cells. The IP address is not a property that the base stations care about at all,

Every single mobile network will maintain IP addresses when migrating between cells. The IP address is not a property that the base stations care about at all, it's generally tied to the PDP context maintained by the GGSN/PGW, which will generally not be invalidated unless the connection is idle. Mobile operators will only have a handful of core networks even in large countries; having a subscriber move from the area covered by one core network to another would be quite rare. Switching between cells will cause a latency spike, and a lot of correlated packet loss if the subscriber has a large queue of undelivered data, but that's all. But handling packet loss and ordering are what TCP is supposed to do. I have no idea of what you mean by "the TCP connection is no longer there". The TCP connection is a distributed system living on the client and the server. It doesn't go away unless one of the endpoints decides so. (Modulo stateful middleboxes, like NATs. But nobody in their right mind would run a TCP state-aware middlebox on a cellular network base station). IP changes are relevant when switching networks entirely, like going from WiFi to mobile.