I've been arround the tableau forms and it doesn't seem to be an easy way to keep the date range filters and also keep the last N days of data.
Our workarround for that was to use a tool called XmlStarlet (free) to programatically edit the workbook default slider values everytime the data is refreshed (our etl tool triggers the proper batch file to do that). After altering the workbook filters, we republish the workbook and run an export to make sure the data is refreshed and not only the default dates.
It's not the cleanest way to do this, but it's the best one we found since you can't set that in the front end. Just to clarify we've been using Tableau Desktop and Server for 3 months or so
I'm attaching a sample batch file with the commands used.
republish.bat.zip 546 bytes