I would let her go as well. If she has said I'm so sorry I've neglected the friendship I've just been so busy but I want you in my life and will make more effort - I would say hang in there.
But her response kind of sounds like a polite brush off from someone that has let go a while ago but can't be honest about it.
If she attempts to reconnect with you, then great. But sadly it sounds like you need to let the relationship go