Yes, there are several options for customizing this behavior. All of them are located at Menu > Setup > Map Settings > Auto-Track Plane.
To stop the map from ever re-centering*, set this feature to Disabled.
Otherwise, you have further options to control how the recentering* occurs:
Enabled: After the timer expires (the timer starts counting when you stop touching the screen, and will reset to 0 if you touch the screen again before it expires), the map will "snap back" to center* your ownship. You can set the Auto Resume timer to be 10sec, 30sec, 1min, 5min, or 10min.
Enabled when Moving: If iFly detects that you are stationary (like sitting in a chair doing flight planning), then the auto-centering* feature is inhibited. If you're in motion, then the map will snap back to your ownship when the timer expires.
* "Centered" means your ownship will be in the center of the screen, IF "Center Aircraft (no skew)" is checked or if you are not moving. If this option is unchecked and you are in motion, then iFly will skew the screen to reveal more of the map in front of you and less of the map behind you (so your ownship is not exactly "centered"...perhaps "focused" could be a better term).