Forgetting a network

I'm not sure what you mean by forgetting local home hubs? I believe if you reset your network settings to default though, that should clear any networking information on the console, to do so:

Restore Network Defaults

1. Press the Guide Button on your controller, go to Settings.

2. Select System Settings then Network Settings.

3. Select Wired Network or your wireless network when displayed.

4. Select Configure Network then Additional Settings tab.

5. Select Restore to Factory Defaults then confirm when prompted.

Hope that helps!

Forget and Reconnect to the Hotspot:
On your Xbox One console, you might want to "forget" any previously saved Wi-Fi networks and then reconnect to your iPhone's hotspot:

Navigate to "Settings" on your Xbox One.
Select "Network."
Choose "Advanced settings."
Select your Wi-Fi network (if listed), then choose "Forget."
After forgetting the network, you can attempt to reconnect by following the steps to connect to a new Wi-Fi network and selecting your iPhone's hotspot.

That is a network security setting, it is like telling your console to forget network when you disconnect.

Just like on your phone, if you tell it to forget network, you'll have to put in your password to re-connect.

I have heard of other people having this issue with Destiny specifically. Many times you can fix it by holding the Xbox logo on the front of your console for 10 seconds until it fully powers down and unplugging the power cord from the back of your console.
Leave it unplugged for 5 minutes, plug it back in and set up your network again. After that it should hopefully keep your information.

I am seeing the exact same behavior. In the middle of playing Destiny, the Xbox One will disconnect, and Settings will indicate that no wireless networks are configured. This started in the past few days.