Problem with my bras.Is this true?

I'm a 17 year old girl and I wear a 40 DDD in bras and it seems that whenever I try on bras it fits me perfectly the first time but sooner it stops giving me support. It has happened to me for all my bras.A woman I spoke to about this problem told it me it was because of my large cup size and that's harder for full chested women to keep support in their bras. Is this true? Is There anything I could do to stop this problem?