What do you guys think I should do with my rabbit? :(?

I just got a rabbit a couple of months ago and recently she hasn't been as happy as she should be. And she just can't seem to warm up to me, no matter how often i play with her orr how hard I try. I just got a part time job, and i have taken up guitar and between those things and my schoolwork i feel like shes not getting the attention she deserves. Also, she may be making my moms asthma act up. So my mom proposed that i give her away to a family that will take better care of her, but i kind of feel like a failure if i give her up, and i do love her. But i feel like she's not getting the right attention here. So do you think i'd be a failure if i gave my bunny up? please help, im really confused.