Diagnosis
The camera is stuck in setup mode because it can't establish a stable handshake with your Wi-Fi router. This is almost always a signal strength issue.
How to Fix It
First, move the camera much closer to your router, like in the same room. Go through the setup process in the Ring app again there. If it connects, you've confirmed it's a range problem. For the permanent spot, you have two good options: 1) Get a Wi-Fi extender that creates a new network closer to the camera's location, or 2) Use the optional Ring Solar Panel accessory—it has a built-in Wi-Fi repeater that can boost the signal specifically for the camera.
If That Didn't Work
Check if your Wi-Fi is set to the older 2.4 GHz band. The Stick Up Cam Battery cannot connect to 5 GHz networks. Most routers broadcast both; you may need to temporarily disable the 5 GHz band in your router's settings during setup to force the camera onto the right one.
Heads Up
Don't just look at your phone's signal bars in the spot—your phone is a more powerful receiver. The camera's antenna is weaker, so it needs a stronger signal than you might think.