This was EXACTLY the [roblem I had with an earlier build. Basically, running the game in stock mode was fine, full joystick function.
Then, after installing 3.55 ( I think ) and the then current version of launcher, no joystick anymore.
I ran through a similar process with Random Tiger sending me an assortment of launcher variations, and me feeding back error messages etc. to try and get some kind of data as to what the root cause was.
Then....I had to do a complete re-install of Windows XP after a failed attempt at setting up a dual boot system ( never going to do that again!!!

)
BUT here's the odd bit... I re-installed FS2 and ran a single stock mission to test the stick was working. Then I downloaded and installed the latest stable build ( as listed in the latest version of everything thread ) and launcher, and the stick worked!!!
I had installed XP, and was using the drivers that were loaded by XP for the stick ( a Saitek Cyborg 3D rumble force ). This was, as far as I thought, the same setup as I had before re-install. Only now it worked as it should.
Perhaps a complete clean re-install of FS2 helped....I really have no idea!!!