I'm very happy with the new ethernet code, I don't have any problems with subsequent connections anymore! My code has been running for more than 48 hours continuously, sending an HTTP request to a webserver every 5 minutes.
However, my Arduino froze two times up to now, both some time after the webserver to which the request was sent became unavailable. I don't know exactly after how much time, but I guess it is around half an hour. Does anybody of you have any idea what could be the cause of this?
BTW, previously I had another problem that when my sketch became too large (> 11k) every connection resulted in a frozen Arduino (using the new client code). I "solved" this my reducing the sketch size (removing debugging Serial.print statements).