You might want to check your iptables rules on your server. It sounds like you've a rule for limiting new SSH connections.
The next rule allows 5 new connections per minute, if you exceed this limit, your new connections will be rejected after some time has passed:
-A INPUT -p tcp --dport 22 -m conntrack --ctstate NEW -m limit --limit 5/min -j ACCEPTSee the IPTables / Netfilter documentation, scroll a bit till limit.
