I called the backdoor number over at Cap One today to inquire about a CLI. I just had luck with HSBC today and I have not received a CLI from Cap One since July. Needless to say, they would not give me a CLI and told me to try again in 3 months. A little frustrating since I have had this card since 2001 and the CL is only at $1200. My APR has always been at 15.9%, which is much higher than my other cards now so I figured I'd try my luck at an APR reduction. The CSR was very pleasant and said she would take a look at my rate. A few seconds later she said that my rate was too high, and she would immediately reduce it to 11.9%. Not bad by today's standards (not as good as my JUNI M/C which is 7.9% though). I then asked for my annual fee to be eliminated. Capital One is the only card I have now that charges me an AF.
She immediately responded with "Sure, we can get rid of that fee". So although I did not receive a CLI, I still managed to get my APR reduced and annual fee eliminated. Not bad!!
With most creditors, 3 to 4 months is a little too soon to ask for a CLI even if they are short changing in you in the first place. I recommend 6 months starting out, and 6-12 months if you have had a card for quite awhile and already have a high credit line.