It sounds like you are recieveing the short straw from the "Instant-On Power Mode"
In this mode, your console will stay in a low-power state, even when turned off. This allows it to turn on quicker, and will also permit it to download any update it requires, regardless of whether your actually there.
If you were to boot the game up from scratch (where the game loads itself up and takes you to the main menu), the Xbox would check for any updates, first. For online to work properly, all users have to be running the same version, so generally you are forced to wait for the update before you can play. If you are already in the middle of a game, and are loading straight to where you left off, you are bypassing this check.
Naturally, the update keeps going. It has already been told to download and install from the power option. As soon as it is downloaded, it asks you if you want to install it. If you do, the system needs to reset to make sure everything completes properly.
First Solution: You said it asks you if you want to install the update. Have you tried selecting No? From my use of the console, it should come up with "you will not be able to play online" until you exit out and allow it to install the updates. But your single player game will continue, and any progress that saves online will simply wait until the connection is reestablished.
Second Solution: Disconnect your Xbox from the Internet. Ask if there is really a good reason for it to be connected, in the first place. If you are not using any feature that requires internet, this might save you from accidentally using download limits, simply because your Xbox decided to pre-load an 80GB game you don't intend on playing for a few weeks.
The link I provided will also direct you in how to disable Instant-On. According the Microsoft, the other option has three distinct differences.
Energy-Saving Power Mode:
- Xbox will take 45 seconds to turn on (up from 2 seconds)
- Xbox will not be able to turn on with voice commands
- Xbox will only look for updates when you turn the console on
You will still have to update, but I understand that you should be prompted to download it, in the first place.
One thing that isn't mentioned, that I think may be impacted on, is your ability to jump directly back into the game. If the console is not retaining some of its power all the time, I question whether it will be able to remember exactly where you were in Batman. Instead it will likely make you restart the game, much like an older console.
If you are having troubles past that, I recommend getting in touch with Microsoft Support. That page has a lot of different categories, so you can easily familiarise yourself with various features. For example, if you did not know what Xbox Live is, you may want to look in to "Xbox Silver vs Xbox Gold" and the "Games for Gold" program. Down the bottom, there is also a handy "contact" button, that streamlines contacting the right person for the right solution.
TL,DR: Check here and change your power settings to energy-saver, contact Microsoft here if the problems persist.