Well... If she's constantly trying to kill herself, she couldn't be trying very hard...
Not to make light of the situation... But the fact that she's able to keep making attempts, and keeps making a point to tell you about them, might suggest that she's really not all that committed to killing herself, and this may just be a cry for help... I mean there's very few ways to seriously attempt suicide that don't work, and don't end up hurting you enough that you need hospitalization.
Either way, call the police, tell them the situation, have her taken to a hospital and assessed. She's obviously unstable and you can't trust her not to hurt herself. That, I think, is the obvious answer
And of course I overlooked the fact that you've already talked her into going to the hospital... Well good... Make sure she actually goes... Take her there yourself if you have to.