Buried in the JavaScript code is a ‘feature’ that turns off the search box if there are more than 3000 items in the index. This is presumably to keep the pages fairly responsive.
You will note that there is no search box for person index either, (there normally is), because you have over 8000 persons. In your earlier release of your tree, there were 2605 media, in the version with the missing search there are 5439.
If you want to see what happens if you change the limit, in the directory containing your html pages, in data/dwr.js file at line 1810 or nearby is the line
var TABLE_OPTIMIZATION_LIMIT = 3000;
You can up the limit to a much larger number, like 10000.