We have had this problem happen numerous. The problem isn't saving it to a CSV file. Rather, it is opening it in Excel (which, I think was what Andrew was alluding to).
Opening a CSV in Excel doesn't invoke the Data Import Wizard; Excel tries to figure out the formats itself, and chooses a numebr format, which of course, drops the leading zeroes.
There are a few ways around this:
1. Export the file from Access to another text file option (i.e., .txt, .prn)
or
2. Export to a CSV file, but then rename the .csv extension to .txt before opening/importing into Excel. This will now cause the Data Import Wizard to be invoked, where you can control the format of the incoming data.