If you uninstall and reinstall Burnout Paradise will you lose your save data

Yes, you'r save files are located here...

C:\Documents and Settings\[YOURNAME]\Local Settings\Application Data\Criterion Games\Burnout Paradise (Win XP)
or
C:\Users\[UserName]\AppData\Local\Criterion Games\Burnout Paradise\Save (Vista/Win7)
Just copy the save files to a flash drive or a different location on your PC so they won't be deleted, and if you want to reinstall Burnout, just drag those files back to where they were originally and you can play where you left off.