I ran into the same problem with a Brother MFC-8710DW. I found a blog post that suggested a problem with spooling, so I tried this:
- Open Printers and Devices
- Right click on the printer and choose "Printer properties"
- Click the Advanced tab, then select "Print directly to the printer".
After that, I was able to print multiple copies just fine.
I don't know if this will work with other models.