I don't know if you fixed your problem or not. But here is how I solved it. Hope this works for you too.
I went round and round with Microsoft on this too. From what I can figure out, Microsoft considers the timeout for the Mobile Hotspot a "Security Feature". However, there is a way around it, but it takes several steps. Steps 1 to 3 MUST BE DONE FIRST. Otherwise you will have trouble sharing the network.
1. In the search field, type in CMD and run it as administrator.
2. At the command prompt, type in NETSH WLAN SET HOSTEDNETWORK MODE=ALLOW SSID=<WIRELESS LAN NAME YOU WANT TO USE> KEY=<PASSWORD FOR WIRELESS LAN>
3. Next type in NETSH WLAN START HOSTEDNETWORK
4. In the search field, type in Control Panel and press enter.
5. If your Control Panel is set to Category view, click on Network and Internet then Network And Sharing Center. In the Icon view, go directly to Network and Sharing.
6. At the top let side of the window, click on Change Adapter Settings.
7. In this window you should see three connections. Ethernet, WiFi, and Local Area Connection*1. The connection that ends with *1 is a virtual connection and the number may vary depending on your computer.
8. Right click on the Ethernet connection and select properties.
9. Select the Sharing tab. Put a check mark in the “Allow other network users to connect through this computer’s internet connection”
10 Finally, select the “Local Area Connection*#” from the Home Networking Connection drop down box. Click OK.
Your wireless hotspot should be up. You may need to reboot for it to work correctly. Also, the wireless network will not startup on boot. I recommend you create two batch files in a convenient location with the following commands.
Wireless start batch file - netsh wlan start hostednetwork
Wireless stop batch file - netsh wlan stop hostednetwork
Those two commands will allow you to stop and start the wireless hotspot as needed.
If you want to have the hotspot start automatically. Open file browser and type SHELL:STARTUP in the address field. then copy your startup batch file to that location. This is profile specifiac, so if you have multiple user accounts, you will need to do this on every one of them.
If you want to remove the hotspot open a command prompt as administrator and type in NETSH WLAN SET HOSTEDNETWORK MODE=disallow SSID=<WIRELESS LAN NAME>