Alright, I would suggest some of the following actions at this point:
Try a FULL power down of the console. Most people tend to use the hibernate/ quick start up mode of the Xbox One, but after the console has been left in this state for excessive periods of time, some games can suffer performance issues.
To perform a full power down mode of the console, you can do it two ways. If you place your finger on the power button of the console and hold it there for at least 10 seconds, the console will shut off completely. If you did it correctly, the light on the power brick will turn from white to orange. The next time you start it up, you’ll see the Xbox One logo flash instead of the black and white logo and the quick sign in to the dashboard.
Another way to perform a full hard reset of the console is to go to My Games and Apps > Settings > Power and Startup > Turn off and Restart > Restart Now. Achieves the same effect.
If the problem persists after this point, I would recommend trying to re-download the packs from the marketplace real quick. Don’t delete them and re-download them, just check if you can download them or if the console acknowledges you have them downloaded.
You can also try fixing your internet connection, which most likely is the real culprit. Trying to reset your modem, and improve your connection speed to the server side can help greatly. If you are downloading anything on your computer or doing anything to divide your connection too heavily, I would recommend trying to minimize as many of these things as possible. Poor connection to the servers will most likely result in a failure at the checking downloadable content screen, and cause this issue.
If, worse comes to worse, and I really wouldn’t recommend this until all other options have been tested, you could delete the game on the console and try to re-download it. Don’t delete your character packs, just the game itself, and download it again. In the past, this has fixed several issues.
By that point, if the problem persists, I would highly recommend working with one of the IG devs either on the forums or twitter, or contacting MS on their customer service line. Usually guys like @TheKeits or @TempusChaoti can point you in the right direction to get the problem sorted out as quickly as possible. If it is an issue with the game, and nothing on your end, then it’s something they should know about and be informed of right away so it can be fixed, as you’re mostly likely not the only victim.
A few questions:
Is your internet fairly reliable and fast, or is it not very powerful and tends to drop frequently?
What speed is your internet? It should be something around 6 Mbps for at least a decent experience.
Are you using a wireless or wired connection? If you are using a wireless setup, and your connection has several walls and a lot of distance to go through, then it’s recommend to move as close to your wireless connection point as possible, or even better, use a wired connection only. Using a wired connection greatly prevents packet loss and further decreases lag and other potential problems.
Do you have an Open NAT?
Whose profile was the game downloaded and purchased under? or really the character packs. Was it downloaded by you or another profile on the same console?
Does this issue arise when you start the game under the alternate profiles on your console?
Some of these questions may lead you to the cause of your troubles.