I would utilise Robocopy for this task (assuming this is a Windows based system). You can schedule robocopy to run overnight via batch job. Typically, I would schedule the job to run on the source server to run under an account with administrative rights on the destination box. There are also a lot of switches you can apply, for instance when scheduling a recurring task you can copy only modified files, etc. I would also recommend you pipe the activity to a log file by adding a >>D:\logfile.txt (for example) to the end of the command, so that you can study what has occurred. It is part of the Windows 2003 Resource Kit Tools, available from the following link:
http://www.microsoft.com/downloads/details.aspx?FamilyID=9d467a69-57ff-4ae7-96ee-b18c4790cffd&DisplayLang=en
Study the switch options available and try on a small set of files first; for instance there is a /R:n switch that sets the number of retries on failed copies - the default is one million (you may want to change this to something like 3!).
I have found robocopy to be one of the most useful bulk copy tools available.