The LTE signal is very fragile. What you're experiencing isn't implausible. For instance, I have two towers approximately equidistant from my house. One is an active LTE tower. The other is in the process of its upgrades (and may be slightly closer; I don't know the exact location of either tower). At my house, I can connect to LTE on the active tower, but only for a minute at most. I'm assuming it's because the phone is trying to connect to the closer, unfinished tower and getting rejected. The LTE signal I get at my house from the finished tower is pretty weak, "meh at best". However, if I drive just one block closer to the completed tower, I get a steady signal to the completed tower with no disconnects.
My point: One block can make a noticeable difference with LTE signal, especially in a city with lots of buildings and other obstructions, like Chicago. Consider that my story is taking place in the suburbs with no tall buildings in the way.