When my oldest daughter was that age, my pediatritian told me to let her know I was there for her. He explained that since there was no genetic concern for any type of anxiety disorder, and she did not present with any neurological issues, that it might be best to let them cling - and test the waters on their own. I am so thrilled that I followed his advice (not only is he a great ped. - but he's got 6 of his own kiddos)! Although, I still exposed her to groups - it was always Mommy and Me activities - so we did not need to have any separation issues. My daughter thrived - and is currently away at sleep away camp right now (o.k. - so now I'M the one that is crying!!!).
I guess the fact was - all children develop differently. Your concern and interest in helping your child is evidence enough that you are certainly no failure! Perhaps you might need to adjust some of your attempts to help your child...isn't that really a large chunk of the parenthood path? We need to constantly adjust to best meet our children's needs.
Your child is very fortunate that you have her best interest at heart!