I think the decision to keep it up is motivated by a sense of wanting to 'stay strong against the haters'. I'm not in the business of psychoanalysing strangers but if I was in her position, I think I might want to do the same to, not because of the reason both she and I mentioned, but because if she deletes it now, people's vile responses will still be there. Imagine this:
Two months from now, everyone will forget the original photo. Many will still remember the incident and the feelings surrounding the whole affair. An anti-Islam account with 1 million followers screenshots one of these vile, p0rnograh!c responses while the space where the picture would have still been says "This post is no longer available".
That blank space is misused by the anti-Islam user to spread propaganda. They falsely claim that this photo was actually of a niqabi in black whose eyes are covered. "Muslim men don't even like niqabis!". And it doesn't matter if people have screenshots because the story has already caught on like wildfire.
Some Muslims need to have their internet taken away, for they forget the words we type will be asked about on the Day of Judgement just as the words we speak in real life.