Ellipsis or Emphasis?

I find myself disagreeing with the two well reasoned comments above. It need not be temporal at all.

"Not with all I have done for her" will do just as well as despite. All such activity is in the past and as such appears as only temporal. The Not expresses his disbelief of her uncharacteristic response to his earnest efforts.

Despite itself has its own negative, meaning in spite of it or against it. When replaced by "after all I have done" it is natural, though not essential, to add a negation in front of it. That is the reason for the not.

Here is the relevant definition of after in the online version of the Cambridge English Dictionary.

following in time, place, or order:

• After (= despite) everything I've done for you, is this the way you treat me?
• After (= because of) what she did to me, I'll never trust her again.

In fact, as you can see from the words = despite and = because of that after does have a causal or concessive use.

Now it might have been more typical to have omitted the negative not:-

I can't believe she'd do that after all I've done for her

But the speaker has instead repeated the negative in I can't. It is a rhetorical device of repetition for emphasis. Here what is being emphasised is the disbelief. It grabs the audience's attention, just as it grabbed yours.