Switching between device profiles won’t cause the calibration/alignment parameters to be lost. If you are physically moving the camera between machines, you’ll need to re-run the alignment step (but not calibration) with each move.
If you’re not moving the camera between machines, but the camera overlay is becoming misaligned between uses, it means that the position of your camera relative to your workspace has changed from when you did your initial alignment. How are you mounting your camera? Make sure the camera is securely mounted with no wiggle.
If you switch to a thicker or thinner material and do not have an adjustable height bed (I’m not aware of any diode laser which has one), that can cause a misalignment, as the height between camera and workspace will have effectively changed. Make sure the laser itself hasn’t moved at all - sometimes engraving motion can jostle the entire laser.
You’ll need to address these issues, and then re-run your alignment.
Here are some resources on the camera alignment process. Please review them to make sure you completed your initial alignment properly.