You need to be very careful, as you're probably already half-way through the original veneer depth. What may be happening is that you are now seeing the bottom layer of the veneer that's absorbed some glue where it's been stuck down. So it's probably not going to absorb much more stain, and more sanding will remove some more of what little veneer is remaining, lightening it even more.

Have you tried brushing on a very strong dye solution to just that area? Be careful as you don't want to create a darker ring around it.