I was holding a DJ performance with rekordbox (iOS/Android) and a XDJ-RX connected, but when I used the phone or another application on the mobile device the performance was interrupted.

When rekordbox (iOS/Android) is running and the telephone or another application is used in the foreground, rekordbox (iOS/Android) processing continues in the background. However, applications running in the background may be suspended or stopped due to iOS or Android operating system control.
If you have used the telephone or another application, quit it promptly and set rekordbox (iOS/Android) back to the foreground.