I use the ASE regularly so I was annoyed when the 1.03 patch went and broke the connection support that 1.02 fixed.
But luckily a fix has been posted on the ASE message board, and I think its worth sharing with any BF2/ASE players that may visit.
You need to right click on Battlefield 2 in the ASE, Custom Config, and after the CMD line, such as "C:\Program Files\EA GAMES\Battlefield 2\BF2.exe" you specify your BF2 account username and password.
For example:
"C:\Program Files\EA GAMES\Battlefield 2\BF2.exe" +username RichGC +playerPassword MYTOPSECRETPASSWORD