I have only done one recon and that was with barclay. I did not get the denial overturned. They were not happy that i had about 7 new accounts that were less than a year old. My credit score at the time was 705 on TU. They simply told me that i could apply again once the accounts were over a year old with no guarantee. So this was for the arrival + card.
Once my accounts passed the year mark the Jetblue barclay card was out and my score had jumped to 755 on TU and i applied and was instantly approved.
Also as a data point i called back a few different times to see if i would get a new rep that maybe would have a different decision. Needless to say i stopped calling once they told me " i see you just called about this 30 minutes ago. LOL. Good luck.
