How does one say sorry for breaking a promise to an 8 year old?

I recently moved from my family hometown(mom, dad(married and living together); sister(married to a great guy), and brother and his wife(of whom’s children I am speaking of)). Long story short, I promised my niece we would be pen pals. Obviously I fell through and did not send the initial letter, but I despretly want to be involved in her and her siblings lives. I have been going through some stuff that is hard to explain to kiddos her age, amongst other things: depression, lack of self worth…
(more… they all connect). I do not want excuses to tell them, I have a million, I just want to make her feel special and let her know i think she and her sister(4 years) and her bother(1 year, 6 mon) are smart and special to me. How do I say this besides saying what I have already said(i love them, i am sorry,.....) I am scared, don’t want to lose them, I feel like I am too late…