ssh: too many connections in short succession?

I'm running a backup server using rsnapshot, which uses rsync, which uses ssh to connect to the hosts from which to gather data. Usually, everything works fine. I run in to issues, however, if very little data has changed, and if there are a lot of separate directories to be backed up (more than 5). I figured out that the issue is ssh, which can only connect five times within roughly minute, then I have to wait again before making another attempt. This script demonstrates the issue:

#!/usr/bin/bash

for j in {1..3}
do
    for i in {1..6}
    do
        ssh my.server.xyz 'exit' && echo "ok #${i}" || echo "failed #${i}"
    done
    sleep 60
done

The output looks as follows:

ok #1
ok #2
ok #3
ok #4
ok #5
ssh: connect to host my.server.xyz port 22: Connection refused
failed #6
ok #1
ok #2
ok #3
ok #4
ok #5
ssh: connect to host my.server.xyz port 22: Connection refused
failed #6
ok #1
ok #2
ok #3
ok #4
ok #5
ssh: connect to host my.server.xyz port 22: Connection refused
failed #6

Is there some sshd option to configure this limit of 10? I'd like to be able to do up to 10 connections from the same host within a couple of seconds.

I figured out that it has not really anything to do with ssh, but with IP tables on the server (where sshd runs):

# iptables -S | grep 22
-A ufw-user-input -p tcp -m tcp --dport 22 -m conntrack --ctstate NEW -m recent --update --seconds 30 --hitcount 6 --name DEFAULT --mask 255.255.255.255 --rsource -j ufw-user-limit