Her birthday was there and she wanted to meet but for some reason I was unable to meet her whole day!!
She thought I didn't wanted to meet her...
I told her reason but she feels it all fake reason I am giving her
HELP ME OUT GUYS I Don't Want to LOOSE HER

Let her cool off, and see for herself that you did your best.

Give her some space, then in a week or something try to explain and apologise again.
If she's still angry, maybe you need to let her go...

I would try your best to calmly explain again. Giving her space will only allow her to think that you either 1) gave up or 2) Lied.