It is hard to know exactly why but based on your description, I suspect your hosting provider has some sort of limits in place which limit the number of emails you can send during some time period and/or there is a limit to the number of email addresses which can be sent at one time. This is pretty common.
There is no solution for scheduling messages if your hosting provider limits how many emails can be sent in a specific time period. There may be other plugins which queue email but Email Users does not.
If your hosting provider limits the number of email addresses which can appear in the email header, there is a BCC Limit setting which will break the group of recipients up into chunks and send the least amount of emails it can while staying under the limit.
Check with your hosting provider to see if either of these limitations apply to your situation. It is also possible you have another plugin which plugs into wp_mail() which could be causing a conflict. I’d check the limits from your hosting provider first.
