This is your code, modified to use binary search (so it’s much quicker).
http://jsfiddle.net/thai/zkuGv/4/
It begins at 1 pixel and doubling its size until the it hits the maximum (I use 253, which is the biggest integer that can be stored in JavaScript without losing precision and would make the binary search buggy), or the div collapses to zero pixel.
Suppose we set the div to size h and it disappears, then the maximum size must be between h/2 and h. We binary search from there for a height h that does not make the div disappear when set to height h, but disappears when set to h+1.
Then we can come to a conclusion for Opera: 2147483583 pixels.