If you use 1 to 1 chat, you need to logout from Chat when application goes to background and login again when you go foreground. In this case messages will be delivered without any issues.
In case you are using chat room, you need to enter the room in order to receive message history.
If you wish to implement this logic, you need to join particular chat room when application comes from background.
For example, if application goes background you need to exit the room, then QBChat instance.
When application goes foreground you need to join QBChat instance, then join chat room. As a result, you receive the full message history.
All these actions are not shown to the users.
More information you can find in our official documentation: QuickBlox Docs
Choose the Chat option from the left sidebar menu for one of QuickBlox SDKs and the Advanced section.
Then select the Offline messaging section from the right sidebar menu.
If you have any additional questions, feel free to submit a ticket to our Support team and we will help with all your efforts.