Known problem, ASUI does start/restart after installation/upgrade but then appman stops it for some reason. You can see this by enabling the start_visible setting. It however works fine when installed or upgraded from the console.
I was only able to reproduce with the screen locked but still on, it only happens when its on right?
Power button to 'unlock' is a feature!
What is the name of the init.d file that starts dropbear, what is the full path to the server binary and what is the full name of a client process (do they start with "sshd: ")?