She doesn't want to sleep, but her body gives her no choice, and since she can't wear the twisted ring anymore, there's not even the chance of reaching Angie that way.
Warding her dreams would be a waste of time - it's hard to imagine anything waiting for her worse than reality. Angie's missing. In trouble. Hurt. And she's completely powerless. It's only the distant thought that Mesaana could discover she's still alive that makes her form the weave and then she's reluctant to let go of saidar, feeling the joy and life and strength that the Source brings, but she does right before she falls asleep.
( Searching )