Fallout Shelter Losing Resources After game is Closed

Solution 1:

The game does continue to run for a little while after you leave. This is to encourage players to play for extended periods of time instead of just quickly checking on their vaults. You need to make sure that you have enough resources to survive the period in which the game runs yet you aren't online.

I would check that you have enough storage. You might not even have the capacity to store enough resources to survive closing the game.

Solution 2:

Are you sure you are completely logging out of the game?? Don't just click the game off. Go to the bottom right corner and click on the pip boy. The first option lets you log out. Click on the gears symbol then main menu. After that you can click out of the game and it won't keep running forever depleting all resources.