I have the latest AIR SDK version 25. My minimum iOS version is set to 7.0 so I don't have to bother with the old 6.1 icons.
And Flash Builder won't publish the <image120x120> icons. People were complaining about this issue 4 years ago and it's still there.
Not only that but Flash Builder renames all the icons to very old versions, and won't even LET you include the new pList icon bundle keys yourself -- it complains that these are SPECIAL files that have to be under an <icon> tag. So not only does it get them wrong, it won't even let you set it up manually.
Move icons to an icons/ subfolder and use non-standard icon names. Link these in app.xml.