Different times for different lenders. Kroger 1-2-3 (through RBS Bank), told me 9 mo. min. before requesting a CLI. While Best Buy will consider one every three months. Just the nature of the industry.
Starting Score: TU 737 EQ 721 Current Score: TU 741 EQ 741 Goal Score: TU 765 EQ 760
I think it also depends on the type of account. Store accounts will encourage CLI sometimes more than major cards because it helps drive product sales, whereas the major card is "cash out" cost and risk without the benefit of selling store products.
If I can try for a CLI without it being a hard I try every 4 Months. If it will result in a hard and the CC never give auto CLI's I try once per year. Other than that I just wait for the auto increases. On certain cards I'm willing to risk the inquiry for a CLI.