Is there a way to permanently "Deny" an application incoming network connections (i.e. no more prompts)?
No not really, when you open a program whatever core process it calls into action are run every time. One of which will, in your case, checks on the various permissions it has to make or accept outgoing/incoming connections. The act of double clicking and opening the application (even after choosing to deny such privileges) will overwrite/trash your past decisions to DENY incoming/outgoing connections simply because you gave it permission to open (not when you ACCEPT though - in this case any previously accepting connections will not continue to ask for your permission).

Unless there is a setting within the application's "Preferences" or you change some code within the "Contents" of its bundle then it is highly likely that it will prompt you every time.

BTW these permissions requests are meant to alert and pop up every time to keep users from making "permanent decisions" (AKA turning off popup notification and permission requests). Without the popup requests, switching permissions settings back and forth would become a much more difficult task and more than likely need the help of a genius bar rep to switch them back and forth (for the not-so-savvy users at least).