I use the custom area function to create my saved searches and it takes a while to get it to include exactly the areas I want. Then if I change my mind about some parameter of the search (e.g., I had a saved search for the Caribbean for any dates and wanted to change it to just winter), I have to delete the existing saved search and start over trying to get the area right.
There was another post recently asking for the ability to sort and filter saved search results, which 100% endorse, but we should also be able to save some of the updated filters if we want to.
As a side note, it would be nice if saved searches had the option to exclude sits that conflict with already booked ones. Some people may want to see those sits to save them for later, but I would want the option to narrow down my notifications to only receive the ones I could actually do.