When we're bleeding to death, and about to die, can we add numbers like Strong soul feat, or the lesser soul ring +1 against death to help us survive? I think The Strong soul feat atests an abnormal strong connection to life and should be added into our roll for survival.

It's saving throw versus Death magic, not dying.

The death saves is the strength of your soul opposing to the force that is ripping it out of your body. Nothing even close bleeding to death :D .