We have experienced similar problems with version 0.99.11 that comes with Redhat Enterprise Linux 4.

If I'm not wrong, it appears to be related to the number of file descripters available to the dovecot user. To abate the situation, we stop the service, kill any remaining dovecot processes (some hang around), and then restart dovecot. Sometimes it appears that the limit of connection processes isn't honoured (as defined in the conf file) so the number can spiral out of control.

I hope this helps in the absense of a workaround.

Let me know if there is an obvious configuration setting to remedy this.