On my own hosting server, the script timeout is 60 seconds.
They allow up to 200 emails per hour, and 2000 per day.
At 1 second intervals between messages, the maximum I could send was around 70 messages.
When I reduced the interval, I can send over 200, but I can then reload the page and send another 200.
So I don't think the sending limit is the problem, more the fact that the script is timing out,
I think with my client, the shared hosing may be taking longer to respond during busy times, so with a 60 second timeout, could this shared hosting be a factor ?
In the meantime, I will try your sugggestion.