The latest stable qt version is the split 4.4.2, but app-admin/keepassx-0.2.2-r1 still uses the old monolithic dependency and checks for USE=png, which is not available anymore (enabled by default) in Qt 4.4. Please update the app-admin/keepassx-0.2.2-r1 ebuild, or remove it and make 0.3.4 stable.
Just ran into this today, myself. I just removed png from the build_with_use check. It worked.
Thanks for reporting, stabilization of keepassx-0.3.4 is handled at bug #256415.
Closing since keepassx-0.3.4 is stable now.