just adding my experience
I called for my application for BA chase visa today which I applied on feb 14th . I was told it has been rejected for too many inquiries in last 6 months. I had a gut feeling that I will get rejected. I had applied 2AA, 1 delta, 1 charles schwab all in october and were approved and one more CHASE freedom in december so basically 5 in last six months. I was asked , why particularly interested in this card, and why I have too many inquiries. I tried to explain that I got those offers in mail and just couldn't resist .I offered them to close my other account and That I have always paid in time. But still they said since I had so many inquiries so they cannot give me this product this time. Denied Tough Luck!!