Have you tried giving her a cuddle/rocking her (rather than settling her in the cot). Sometimes with DS, I need to settle him in my arms, then put him back into the cot once calm - then do patting/forehead stroking if necessary.

It sounds like she is not sleeping longer than one sleep cycle (40mins) - ie. she is not self-settling into a second cycle. You may need to teach her some self-settling techniques. Rather than BF'ing her to sleep, have you tried putting her in the cot to fall asleep herself? I have started doing this with DS & it has worked a treat. First, he started to fall asleep by himself, but was still unable to re-settle when he woke up. Now he is able to do both - put himself to sleep (with some help! - patting, putting in a dummy, etc) & resettle after waking up (sometimes with help, sometimes by himself). Here is a thread about what I've tried with DS.

Also, have you tried offering water, rather than boob, at night?