Fascinating. I use Win 10 and I played around more after seeing your comment, Ron. If I start the cursor in open space, then move to "Search," and click, without crossing over anything else, then to the big box that opens, then back to open space, without the cursor crossing anything, I can repeat the process 50 times and the "Advanced" option will not stop its disappearing act. However, If I pass over the ads or anything that is not open space, the "Advanced Search" will make itself available to open.
A to B to C to A to B, etc., as many times as desired and the Advanced does the disappearing act.
A to B to C to D to A to B and then clicking on it works. Strange. But interesting.