First things first; Logically*
Well, we've seen throughout the entire Bleach series that characters can get pretty much assassianted, and pull through in the end.
Hell, it's happened to Rukia like, a million and two times.
(See: Grimmjow putting a hand through her chest.
Kaien-look-a-like [Whatshisname] skewered her on his trident.
Another million occurances.)
Anyway, They're Shinigami. Shinigami have higher tolerences of injuries before they die, either from blood loss or whatever. As seen with Ichigo, Rangiku, Hiyori, Renji, Kenpachi, etc. etc. ETC.
We've also seen Shinigami either stop or slow bleeding with reishi, and that one Vizard guy used his ability on his arm to stop it from bleeding out in the Arrancar Arc.
So, logically we have about five minutes to live or so, before we die of blood loss, or have our heads crushed by something, since I'm not going to bother in making Ame stop the bleeding, because she'd prolly not know how.
Whatever comes first really.