Blend If Layers Disappearing

I took a photo of my dog but realised that his fur could use a clean up. So using a blend if layer, I was able to take away the dirt look.

However, whenever I save the image as a JPEG, the whole blend if layers disappear, going back to the original image.

Here is what I mean:

You can see here what the original image looks like, all layers (apart from background layer) made invisible

Then we have all layers made visible, to see what changes I made

So I go to Save As... and then save as a JPEG. The result is below.

No blend if layers present! Fur is back to being dirty. So I tried the CTRL + ALT + SHIFT + E method to merge layers. Below is the result.

Again, no blend if layers present in the merged layer.

What am I doing wrong here? All blend modes of the layers are set to normal, I have just moved the sliders in the Blend If sections of the layer properties used to whiten the fur. How can I save it so that the whitening of the fur can be seen?