Mass emailing invoices with APR

I have a customer that is emailing out anywhere from 200-400 invoices each morning via APR. the issue is after a while the process chocks as they start stepping on each other. so some will go and others will just fail. recommendation was put these into smaller groups so the printing can create a process which will only deal with a small amount then go to the next group. Is anyone else doing this volume of emailing and did you experience similar issues and how did you resolve. Would love to help my customer out on this with some ideas.