Out of control Aphids

I am so frustrated with all the aphids that have suddenly appeared all over my cucumber plant. They are on almost every leaf and seem to have shown up over night. With my cucumber plant trailing over my tomato plant and currently full of growing cucumbers, I didn't want to spray it with anything harsh. I have sprayed it with a soap 3 times now and the aphids just keep coming. I am afraid that I might have to cut the whole plant back! Some of the leaves are already showing distress. Today I started to hand spray all of the leaves with water. I'm not sure if I will be able to save it.

The picture below is before the aphids attacked.