OK, I think I found the root cause of this. It is obviously not Bluetooth, although this is required every time you connect for the first time or reconnect.
To reassure Daemon42, I am not using the S50's WiFi but my own home WiFi to connect. Using a third PC computer I constantly pinged the S50, which again serves to confirm that I am using my own WiFi. I did the test during the day in Scenery mode but it does not make a difference. As soon as I moved away from the S50 to a different room, the connection dropped, then it reconnected as soon as I got back within range. All this time, the ping test on the third computer showed that the S50 was still connected.
The cause of the problem was a WiFi repeater, which very ironically, I installed trying to improve the WiFi for the S50 when used outside the house. As soon as I stopped this repeater, the ping to the S50 started to fail, then after a few seconds it started to work again. With the repeater off, the SeeStar app on the phone did no longer disconnect as I moved through the house.
The explanation is that the S50 was always connecting to the repeater, while the phone was connecting either to the repeater or the router as I moved away from the S50.
The lesson here is that while a repeater can be used to extend the reach of the WiFi, it does not necessarily extend the distance between the S50 and the phone with the SeeStar app. I do not see a way to control whether my phone connects to the router or the repeater, so it looks like I will have to give up on using the repeater, at least during the nights when the S50 is being used.
