If you're installing to a location where Windows requires elevated privileges, like Program Files, you'll need to have admin privileges to continue.  Are you using an AIR based native installer or have you taken the application with the captive runtime and rolled this up in your own installer?

Here's a section from the Installation and deployment options in Adobe AIR 3 article that might help:

Installation privileges

When designing an installer, one has the option to choose from approaches that may or may not require administrative privilege. For example, a drag-and-drop install on Mac OS X requires no special privilege; users can always copy the application into their own application folders, for which they have the necessary permissions. On the other hand, if registry keys must be written to the machine-specific portion of the registry on Windows, installation of that application will require administrative privilege to do so.

The two installer formats directly supported by AIR, AIR files and native installers, have always required administrative privilege. This was a design decision made in part to simplify the implementation of the AIR installers: If administrative privilege is assumed to be available, implementation is possible if the registry can be written to, and so on. It was also selected because, in many enterprises, this is the desired behavior: administrators can use the privilege requirement to gate software installation.

All the same, there are scenarios where supporting installation without requiring administrative privileges is desirable, or even necessary. This can now be achieved using custom installers; you simply need to author an installer that operates correctly with only standard user privilege. In practice this can be easy to achieve; a simple install-by-copy to a writable location (that is, in the user's own folder) will suffice. Should you author a more complex installer, you should keep in mind that the addition of certain operations during the install process will in turn reintroduce the requirement for administrative privileges.

Could the app be writing files to locations that might need elevated privileges?  Any chance you could zip your app up and send it to me so I could try it on one of my systems?

Thanks,

Chris