Kick it to the curb, as ragcajun would say. Hey, it's like a love interest--if they aren't gonna love you, they aren't gonna love you. Life's too short to keep trying to show them the error of their ways.
Anyway, I know you're talking about automatic CLI's for people with (ahem) respectable credit profiles and well-established accounts, but as smallfry mentioned, they seem to want to see lots of activity, approaching the current CL. That's what the rep told me when I tried to get my CL raised enough to buy an entire refrigerator, as opposed to a couple of ice cube trays. My bad for being responsible, and keeping my balance low, and paying more than once a month. He said that if they don't think you need and will use the increased credit, it isn't coming.
They're a different kind of duck in CCC land, it seems.
* Credit is a wonderful servant, but a terrible master. * Who's the boss --you or your credit?
FICO's: EQ 781 - TU 793 - EX 779 (from PSECU) - Done credit hunting; having fun with credit gardening. - EQ 590 on 5/14/2007