Flash apps are simply not designed for optimal power consumption. Flash is designed for multimedia apps, which are generally power hogs.
I develop Flash professionally, and I'd never run it on my phone.
There is so much flash content out there on the web, and being able to play flash content on-the-move, on-demand is obviously a good thing.
It's easy to imagine flash apps with network access patterns that aren't optimized for phones. Take any advertisement or analytics system which continually polls the server for more data. This will kill your battery if left running.
How does this compare to some AJAX + a timer? Is it the network call itself that's an issue, or just how that is implemented in Flash?