You can initiate a kinda permanent connection if you open the mobile page in Aurora when you open Aurora. Then your pin code should be available as long as Aurora is running.
We're currently looking into a way to login with email and password as an alternative to the 5 digit code, but no promises.
I normally never participate in forums on this site but I would also like to second this. It's inconvenient to have to re-enter pin everytime. Especially when randomly my phone somehow disconnects and I have to re-connect with new pin in the middle of gaming. If the pin was static and remained the same I wouldn't mind.
It would be great if we had a permanent connection from mobile app to desktop client when we open the app.