Alta does this.

If I am generating the same saved report more than one time in a row, I want GIFTS Online to remember what the last information I typed into the Generate Report dialogue box fields was, including search criteria, so that I don't have to start over from scratch if I make a slight error, or if I generate the same report template with slightly tweaked criteria each time.

Real life example: I run four reports using the same saved report template each month in GIFTS.  One is last month non-expenses, last month expenses, YTD non-expenses, and YTD expenses.  Same report template, slightly different title, only one or two query filters tweaked between each.  In Alta, I can run through these super-quick with a slight tweak to the report title and search criteria. 

In GIFTS Online, I have to start from scratch and reenter all of the title, subtitle, query, etc. four separate times.  If I accidentally miss one slight detail in the title of the report, I have to rerun it all over again from scratch.  This is very inefficient.