Save of messages slow when replica unavailable

We have a setup with a dovecot server + replica. This works fine as long as the replica is available.

When the replica is not available for some reason, the clients can work normally with one exception: the saving of sent messages to their inboxes takes ages. Thunderbird times out and complains (and duplicates the message), mail.app just waits until it's done.

Is there any setting that helps here?

For the time being, I deactivated replication; but this isn't a long time solution.

Thank you for all your work&support, appreciating the doc as well.