Can't add images to my Custom store page

[charmony]

I've created a Custom page in my Store and clicked the "Add Pictures" button. When I upload an image, it seems to hang after uploading (even though the uploaded image appears in the uploaded section). The "Browse" button doesn't come back either, so I can upload more images in the pop-up box. I have to "cancel" out of it, after which the uploaded image vanishes. 

The "upload" button seems to be greyed out even before I upload an image, although it does work when I click it, i.e. it goes through the motions of uploading an image.

How do I fix this?