Does the name 'Connie' for a girl really sound like an old woman?

I love the name Connie for a girl (if I'm having one - I've chosen not to find out) but pretty much every one thinks it's pretty old fashioned and is advising me against it! I love it though and I'm pretty sure I'd go ahead with it but I don't want my kid to grow up hating her name! Or other kids teasing her! I don't understand why no one seems to like it!!