There is a closed thread on the subject. Its most recent post was back in 2013. Nothing since, nor a new thread. Virtually all the examples linked in the thread either are totally closed or no longer use Sliding Doors.

I now have a client who wants it.

So, before I get too involved, is there any negative reason for the silence?

Is there any significance to the fact that I don't see sites continuing to use it?

My guess is that menus like this have just become less popular. Perhaps because it's harder to add a menu item or maybe because it doesn't work well for viewing on mobile devices.

Many times these types of things look "cool", especially to clients, but in practice become cumbersome to build and maintain.