A stab wound to the heart is going to result in three very major issues right away:
* Trauma: While there are supposedly recorded cases of survivors, puncture wounds to the heart have an almost universally grim prognosis. Firstly, the wound required to puncture a heart will also have to pass through the chest, damaging other tissues, bones, and organs along the way. On top of that, the heart itself is quite sensitive to damage, and will begin pumping irregularly or stop pumping altogether if it is damaged. Even blunt trauma to the chest is a concern for this reason, wherein the heart is usually only bruised, or ruptured in the most serious cases.
* Blood Loss: Opening a wound directly into the heart will rupture any number of very significant blood vessels which will bleed internally and externally. Blood is required to oxygenate the brain and the rest of the body, so even if the heart does manage to survive this injury the body will still be lacking a critical volume of blood.
* Shock: Circulatory Shock occurs when not enough blood is reaching bodily tissues. Blood loss is an obvious cause, as is cardiac arrest. The inflammatory response of most tissues in the body causes further circulation problems leading to significant cell death.
Despite the severity of the injury, the real organ we need to be concerned with is the Brain. 75
Most bodily tissues can survive prolonged nutrient deficiency (with permanent damage, perhaps) but the brain is more sensitive. The agreed upper limit on brain survival without oxygen seems to be about 4 minutes, though this is usually in a controlled medical environment; brain damage is still possible in far less time.
Regenerative powers will have to address the major issues right away, and in enough time to mitigate the oxygen deprivation they cause.
* Firstly, the heart and its surrounding cavity will need to be healed. This is a slow process in real life, sometimes taking months even for minor injuries. To heal completely in under four minutes your character will need ridiculously fast healing, something like 43,000x faster than normal.
* Secondly, she will need to deal with the blood loss. Loss of volume under 30% is usually recoverable without transfusion, but anything more will require immediate production of more blood, which will be difficult since blood production requires lots of water and nutrients.
* As long as the first two issues are covered, the Circulatory Shock should be mitigated. Adrenaline might help, but its use is usually for anaphylactic shock, not circulatory.
So, if you're looking for some reason your character should not survive, then any of the above requirements make a perfect candidate for removal. You might also note that if the catalyst for this rapid healing/regeneration is some sort of chemical/hormone, then damage to the heart will prevent its circulation, thus limiting its ability to function.
Disclaimer: I am not a doctor, so keep that in mind. 75