No, it turned out that the button wasn’t going to sleep. I was using the Smart Lighting smart app in the classic ST app to control what happens with a button press. I assumed that the button would work like a toggle. However, when the button is pressed, it can only send a command of “turn on” or “turn off” to the lamp. It cannot send a command to “toggle”. In order for it to work like a toggle, it (the button+smart app) would need to know the current state of the lamp/switch it controls, then send the appropriate command. For example, if the lamp is currently off, the button+smartapp needs to know that the lamp is off, so that it can send the “turn on” command to the lamp.
The problem is that in the classic ST app, the button+SmartLighting smartapp doesn’t monitor the state of the lamp; it just monitors itself for the last command it sent to the lamp. So, if the last command the button sent to the lamp was “turn on”, the next time that you press the button it ASSUMES that the lamp is already on, so it sends the “turn off” command. The problem is that if the button was used to turn on the lamp, then the lamp is turned off using something other than that button, (maybe an automation, or the ST app, etc.) the button will ASSUME that the lamp is still on, and will send the “turn off” command when it’s pressed again, which won’t do anything because the lamp was already off. This is why I thought it was going to sleep, but it wasn’t. It was sending a “turn off” command to a lamp that was already off, or a “turn on” command to a lamp that was already on.
From what I’ve heard, the toggle ability works better in the newer ST app.