Great!
Search for deaths using two surnames is now back.

.... Oh dear, spoke too soon. It's only back if you don't search for a pair of names of which there are too many instances, but it doesn't say how many is too many.
After playing with it a bit, I think you get a result if neither of the surnames exceeds the magic number, but if either name exceeds the secret magic number you get all the deaths for the first name regardless of the second name.
For example there are 223 deaths of Binny and 337 deaths of Sang. If I search for Sang, other surname Binny, I get the right answer, which is two.
There are 1,028 deaths of Buick and 1,603 of Joss, and if I put in both, I get the correct answer, one.
But there are 75,345 deaths of Macdonald. If I search for first surname Binny, second surname Macdonald, I get all 223 Binny deaths, and a message saying, "Your search for 'Binny' with a second surname 'Macdonald' returned too many results. The results below do not account for the second surname. Please narrow down your search criteria."
If I search for Macdonald, second surname Binny, I get 75,345 results and a message saying, "Your search for 'Macdonald' with a second surname 'Binny' returned too many results. The results below do not account for the second surname. Please narrow down your search criteria."
So if either surname exceeds the magic number, which must be greater than 1,603 but I don't know how much greater, you get all the instances of the first surname not modified by the second name.
This is a great improvement on "There are no results for your search", and it is manageable by refining the search parameters to include given names and/or date of birth ranges and/or mother's maiden surname, but it's not ideal.