Is there a reliable way to detect the app responsible for an Airpush ad?
Two points,

Firstly if you just want to stop getting the AirPush ads, AirPush themselves offer two ways that you can opt your device out of receiving the ads. Either:


Install the AirPush Permanent Opt-out app, 
or visit their opt-out page and follow the instructions to enter your IMEI to be opted out.


Secondly I don't think that AirPush is the only game in town doing this. I uninstalled an app a few months ago when I tracked down that it was the one spamming my notification bar. Its ads didn't look like AirPush's and it didn't show up with an AirPush detector. Didn't track down who was providing the ads framework the app was using, I was just happy to get that rubbish off my device, for an app I only opened once a month or so I didn't need that hassle. It may be that these aren't AirPush ads, but one of their competitors. That app I just tracked down by working out which apps I'd installed/updated recently, then glancing through the Market comments to see which one was full of users screaming to get rid of the notification ads.