I had a similar instance except with the AMEX DL Platinum. I was given a $5K limit for some unknown reason (I have several AMEX and other CC's with much higher limits). Some weeks I have $7-10K individual charges, so couldn't put them on the DL CC. I waited the 60+ days and got denied for an increase. I wasn't aware of the moving credit between AMEX cards till a month ago, but when I learned of it, I did immediately. Sometimes I wonder about AMEX's algorithms.

Also the AMEX Platinum's (not the one issued through DL) are charge cards, not credit cards, hence the no PRE-SET spending limit. However I do believe they have a limit, you generally can't go charge a $20,000 expense if its not normal spending habit or AMEX feels you won't be able to repay it in time.