This is an issue that happens to the real Cub as well in an uncoordinated turn. Adverse yaw - your high wing is dragging you into a slip and then one of your wings is beginning to stall. If you watch closely, you'll see your nose is first going up, out of the turn, before it begins to drop. You should add rudder into the turn if you have it. If you are flying a rudder/elevator 3ch setup I'm no help as I've never flown that style.
All planes tend to lose altitude in a turn so you want to pull up gently on your elevators through the turn. If you have no rudder or don't feel comfortable with the left stick, pulling a bit harder will compensate and keep your nose up. "Bank and yank" is a legitimate 3 channel control scheme.
I suspect you might be trying to fly slowly as you are learning. Flying slow is actually hard. Going into a turn with too little airspeed can easily result in a stall. Don't try to turn too sharply. Make some big gentle circles. I don't know the FT Cub in particular, but Cub trainers tend to be slow, draggy and underpowered. Don't be afraid to throw some throttle at it.
Stall recovery:
The Cub should not go into an unrecoverable "dive" but your nose may drop and you might lose altitude. If you are falling and have no control, you are in a stall. You want to level your wings and actually give down elevator to pick up airspeed. Then you can increase throttle and pull up. If you are too low, you will meet the ground before you get that airspeed - so they always say that beginners should fly "two mistakes high".
In a low altitude panic in an RC plane you can often do what you should never do in a real airplane - max throttle, yard up elevator and let the prop drag you up. RC planes are vastly overpowered compared to their real counterparts and the prop wash will give you enough airflow to pull up. Try to avoid doing this unless you think you are going to hit the ground, it's bad practice.