There is hope! Last night my husband asked for a CLI on his $15K card (it's the only one he has with them, but he also has a $10K overdraft line of credit.) He's had his account for 11 months. They gave him the 3-5 day message and he was sure it was a "no" since he had applied for a personal loan earlier in the day and was declined.
But today it shows that they raised his limit from $15K to $16K! That's only $1,000 additional but it's better than being turned down flat.