I went through exactly the same process for the Platinum CC. I had started a Titanium Privilege relationship a few days before that.
Didn't hear anything about my CC application for more than a month! Then, on pestering the agent, came to know that it was rejected!
After a few months I was offered a pre-approved LTF Coral CC, -- "because we know you better now"! How exactly that miracle happened, I'd never know, since they didn't have any more interactions with me in the meantime!
I refused the LTF Coral CC because I was still annoyed with them.
A few days later, Amazon offered me an APay ICICI CC, and I accepted that. It was approved in a couple of minutes without any documents or verifications whatsoever! The limit offered was the same as that for the refused Coral CC.