The T-Online impasse

The DSL-Router I have has this Auto-Reconnect feature, that appears to be only on demand. So if my machine is idling away the connection will be lost and the dynamic IP becomes invalid. I can set the idle timeout to indefinetely, but then T-Online comes in the way...

Unfortunately T-Online automatically disconnects all connections around midnight. Now in my current setup I 'd need to send a packet from "within" to re-establish the connection. This is bad because my G5 should sleep to conserve energy and can't have it running just to send an occasional ping packet. Unfortunately but predictably cron does not execute while the G5 is sleeping.

Is there something the G5 does execute while sleeping, maybe Open Firmware stuff ?