This article explains why you've found your session lost or a port forwarding rule disconnected after you put the app to the background and presents a few tips that might help you to overcome the issue.
Termius, like most other apps, can't run in the background due to a restriction of iOS / iPadOS. Recent versions of iOS / iPadOS stop the app's background processes almost immediately (in 20 or 30 seconds), while older versions would allow them to run for 2 to 3 minutes.
That restriction exists for good reasons: to improve battery usage and performance of your device. However, it may present an obvious problem for users of Termius. Below are a few recommendations to overcome it.
Location tracking
When you make a connection in Termius, your session is logged in History, which provides a log of activity and allows you to add these past sessions as hosts.
If you enable location tracking, it will also allow you to see on a map the exact location where a connection was made. As a side effect of turning on location tracking, your background connections will no longer be interrupted.
Split view on iPad
On an iPad, you can utilize split view for running Termius and another app simultaneously.
screen / tmux
screen or tmux can prevent losing the content of the terminal screen when the connection is lost. However, this tip isn't helpful, when you switch to the background and a port forwarding rule is active.
tmux and screen may not be supported on some devices. Those typically include routers and switches.
Note: With the help of a startup snippet, you can make tmux or screen start upon connection.