Just a data point I can't seem to find if it was mentioned here before. I would like to divulge this because I figured this out myself (I'm sure others have too), when looking for AAdvantage availability, for some reason the desktop version on Desktop, displays more availability (I believe it's specifically stopovers) than even desktop version on a mobile device.
Not sure why it does that but it helped me book a Qantas flight that wasn't showing up on my phone.