Check your server log for specific mail errors:
Admin CP -> Tools -> Server Error Log
How many matching users?
Which mail server are you using? (Default or SMTP)
Admin CP -> Home -> Options -> Email Options -> Email Transport Method
It is likely that your mail connection is failing, is slow, or the number of emails being sent and the time required to send them exceeds the timeout of the request.
Basically try a different mail server:
Admin CP -> Home -> Options -> Email Options -> Email Transport Method
The Default option is recommended and is usually faster if the local mail service has a queuing system. This would be managed by your web host or server admin.