Apple - hotspot stops being detectable

Actually, this is what happens for hotspot.

If there is no active WiFi connection, and you're not in the screen that says "Personal Hotspot", it turns off WiFi hotspot feature completely.

To connect your FIRST device, you MUST be in that Personal Hotspot settings page.

After that, it won't turn off until the last device is disconnected.

If your wireless client is a windows machine, try going to wireless settings , select your iphone's SSID and check off "connect even if the network is not broadcasting its name (SSID)" I've noticed this same problem and oddly, If i have one device connected, I still have to open the hotspot screen on my phone in order to find the access point with a second device. This would indicate that the hotspot is indeed still active, but not broadcasting its SSID.