When I began using the tethering option it would frequently timeout and disconnect...this is a feature according to Apple not a bug. I was finding myself constantly going back and forth tinkering with the settings to get my iPad to reconnect and see the iPhone as a wifi hotspot. It got so frustrating that I would just use my phone to do small quick tasks.
That's when I then decided that I needed a cellular iPad and ended up finding one cheaper that the wifi equivalent.
There are two ways to tether iOS devices to one another. The default - the first option presented - is wifi tethering, and it behaves exactly as you've described. It takes a lot of energy for the iOS device to broadcast a wifi network and so the network shuts off after 10-15 minutes of inactivity.
If you want a longer-lasting tethering option, pair the two iOS devices by Bluetooth and then manually direct one to connect to the other. If "personal hotspot" is enabled on your tethering device, then the tether will run through Bluetooth. The connection will remain active until the devices lose their connection, either because they are too far from each other or because Bluetooth was turned off on one of the devices.
I'll grant that directing one device to connect to the other, and then manually disabling Bluetooth to break the connection, represent additional steps over buying a cellular iPad. They're quick to perform, though, and represent a perk of owning two iOS devices.
The downside of tethering is (at least for the iPhone), it kills the battery, so its not imo a feasible alternative for long term usage.
I used to do Bluetooth tethering while at a workplace where I didn't have access to the wireless network. I'd connect the two devices (iPhone 4S and iPad Mini first-generation) shortly before 9 AM and would keep them tethered until 5-6 PM. While I no longer remember the exact numbers, the surprise was that the battery life seemed barely affected.
Again, this is Bluetooth tethering between two devices that supported the Bluetooth 4.0 protocol, not wifi. Wifi represents a significant drain on the battery.
So you're gonna carry this to power your iPhone. Your iPhone is gonna be used to tether you ipad. So you're gonna carry 3 things when you could just carry one?
You can buy an external battery, or you could buy a battery case (such as the Mophie Juicepack). That way you have your case and backup power for your phone, all in one.
Even though I tethered regularly for a long time and had a Juicepack Air case, I never found myself needing to activate the case due to low battery on the phone.