If you can't stop people making updates to the table while you're exporting it, here's an idea - but it's not elegant.

Use the QUERY= option to cut down the amount of data you're exporting. Run EXP multiple times to create an export in several chunks. I've had to do this before on some large tables, and it works well enough. It's just not as pretty as exporting everything into one file.

The other downside is you can't have DIRECT=TRUE if you use the QUERY= option.

Good luck!