Maybe I'm wrong, but it seems like you're confusing Modes 1 & 2 with "Expert" and "Normal" modes.
Mode 1 means the throttle is on the right stick.
Mode 2 means the throttle is on the left stick.
It is possible to change the Tx to one or the other of these modes and it will stay there through power cycles and battery changes and what have you intentionally change it. Be aware that if you bought it as a mode 2 and you change it to a mode 1, your throttle is now on a spring loaded stick and you won't be able to let go of the throttle without it spinning the motors. Here is a YouTube video showing how to change between Mode 1 and Mode 2:
Normal and Expert mode has to do with the responsiveness of the craft. The Tx will always power up in Normal mode. This mode is a little softer and sluggish for new pilots who always seem to want to bang the sticks all the way and bounce the quad off the ceilings and walls. Expert mode is much more responsive. A slight movement on the stick equals a lot more movement of the craft compared to Normal mode.
Normal and Expert mode is toggled by pressing down on the right stick. But it will always be in Normal mode when you first turn it on.
You can also press on the left stick to disable the flip action. I tend to fly aggressively and frequently initiate the flip command when I don't want do, so I usually do this to disable the flip. Pressing down on the left stick and holding it a couple seconds will turn the LEDs on and off.
Holding the left stick to the lower right and wiggling the right stick back and forth calibrates the gyro on the board. Do this when it's on a level surface. If you perform this on an angled surface, then it will think that angle is now level.
You can calibrate the sticks by turning the Tx on while holding both sticks up and to the left (if in Mode 1, then hold the left stick up and to the left and the right stick up and to the right). The power light will blink red and green. Then move the sticks around in circles to their full movements. Then hold any one of the trim buttons until the light starts blinking red only. Then turn it off and back on.
You shouldn't have to do the stick calibration very often. You're probably not going to be changing between Mode 1 and Mode 2 so that will be a one-time thing if necessary. If you want to fly in Expert mode, you'll have to change to that every time you turn it on. I like to calibrate the gyro every time I power cycle but I really don't know how necessary that is.
Your description of your problem really makes no sense to me. You're saying when you switch from Normal to Expert mode, it loses the pairing? And performing the gyro calibration restores it? If that's the case, then I'm at a total loss as it makes no sense.