Too many concurrent SMTP connections; please try again later.

I use Gravity Forms on a client’s site, and I connect via SMTP settings for a catch-all email address to send mail. However on occasion users report that they try to submit the form which goes through fine, but they never receive a confirmation email. The form is set up to have two separate notifications, one for the admin (my client) and one for the user submitting. The error in the logs is “Too many concurrent SMTP connections; please try again later.”. How is this typically fixed so that it doesn’t occur?