Using the following code to restrict results is not giving the expected results:
<input type="hidden" value="3" name="cat" />
Cat ID 3 is a parent category, and search returns results from a number of the child categories (as expected), but not all of them. I'm not 100% certain, but it seems to be categories with an ID of 91 or higher that don't get included. However, if I restrict the search to any one of the missing categories by their specific ID, the posts they contain show up again, so they definitely seem to be getting indexed.