You can save that user, and it all depends on your approach!
A sub category within my product was showing high churning rates, and I was asked to come up with a solution to mitigate this behavior.
I started analyzing data and trying to get into the user's mind, and I asked myself - why do these users uninstall this product? it's useful, easy to use, and they downloaded it independently. So why do they uninstall?
Eventually I had to show some results, and fight back with the uninstallers!
I thought to myself that a user that has decided to uninstall and walk away from my product has a fixed state of mind. But the great thing here is that no matter what I'll do I can't get the situation worse! he is already uninstalling. What do I have to lose ?!
I decided to approach the users with a custom uninstall screen, right after they click remove/uninstall.
The screen had a neutral figure, mascot if you'd like, in the center of the screen, and two buttons on the sides: Keep and Uninstall.
When the user moved the mouse over the half part of the screen where the "Keep" button was, the neutral figure turned into a happy figure:
But when the user moved the mouse over the half part of the screen where the "Uninstall" button was, the figure turned to be upset:
This simple idea has saved 7% of the users that initially wanted to uninstall the product, but the connection between the figure and the emotion created by the effect caused these 7% users to reconsider the product.
The above screen is just an example, and obviously the figure shown had to do with the product itself, but I would suggest using it when possible.
Think about it as the last stop, last chance to engage your user before you lose him. You have nothing to lose at this point, give it your best shot - gamify the experience like in the above example. You might want to offer another incentive to make the user keep the product (i.e. temporary access to pro version, benefits in gaining status, etc.).
And again, the bottom line is - try it, you can't go wrong!