Do you think I should continued to try to make this friendship work.

I have a friend who i was very close to just like sisters , she was upset with me because i forgot to call her for her birthday which was not on purpose, I apoligize to her over and over to let her know that i was very sorry , at the time i had a lot of things going on and had just lost my mom .I also called her to explain how i forgot her birthday , it seems as if she did not want to talk me or deal with me so i let it go.I still continued to call her ,some were return back ,just because i call her . even though she has express she felt some time of way about it ,i apoligize again for it . when i call her to see how she is doing .I dont received any back , should i continued to make this friendship worked.i dont really want to lose a good friend over a birthday. what else should i do. babe