Not much here, to go on, where bpd labeling goes, and tbh, if she's being treated already for depression, she's under treatment and unfair to toss out labels.

Sounds difficult to hang onto a relationship that cycles in a pattern where you break up for 3-4months at a time.

Her break up behavior may seem manic and full force, yet, doesn't necessarily denote manic depression aka bi polar. ?

Better option may be to get some professional counseling to help figure out why you stay with this push/pull pattern. Sounds like a game of cat and mouse.

Are you long distance to her? Mentioned being on Skype at night time.

Hopefully she's dealing with her sh. The hair part, sounds like she's young and working on her identity.