Like described in the manual part of email settings concerning $maxemails it sometimes is a big problem to send more than 100 (or maybe ~180) email invitations at the same time.
Due to some email server settings the connection will shut down after 30 sec or after more than a specific number of transmitted emails per connection.

Example error: SERVER -> CLIENT: 421 4.3.2 Connection rate limit exceeded

A solution would be to set a pause time of 60 sec i.e. in addition to the $maxemails (i.e. 100).

Limesurvey would send 100 invitations in a row and close connection, would wait for 60 sec and would send another 100 invitations, etc.

That way there would be no need for the survey user / administrator to manually send 100 invitations, wait a bit, send another 100 invitations, ... wasting time in front of a screen.

Another possibility would be to send each invitation one by one and wait 1 sec (i.e.) in between.

Third alternative could be that limesurvy acknowledges the error code 421 (see above) and resumes sending after 30 (i.e.) sec.