I have not been flying very long. I only got my licence in March. So I don't have the luxury of time to think about feeling uneasy. My head is still full of trying to get it right.
I used to do a lot of skydiving filming (about 1200 jumps). It was easy to me, I would think nothing of strapping a camera helmet to my head, climbing onto the outside of an aeroplane at 13000 feet then diving off after a bunch of craters looking for a grid square.
I used to get those same feelings you mentioned. Even though I had packed my own 'chute, 'dirt dived' and gone through all my emergency procedures in the plane.
I think once the job becomes easy there is the possibility for complacency and your brain subconsciously recognises that.
The feelings you mention are perhaps your subconscious giving you a bit of a reminder.
I found that if I changed my routine for a bit (ie just did some stupid fun jumps) the feelings left.