Mac setting?> keep trying until reconnect on PPPoE on loss of connxn

I have Verizon DSL for my studio Mac which I’m using as a test bed. It’s your basic cheap consumer DSL which doesn’t give one a static IP, and as it happens the IP gets changed out from under me on average once every 2 days or so.

To allow me to connect as need be from an exterior location, I have a system set up where it checks every 30 minutes and compares current IP with what it had on previous iteration, and emails me the new IP if they differ. That’s worked well but stopped working this weekend (could not connect, did not receive email giving me the new IP).

Came up here this morning and found the problem is that it was sitting there with no IP at all; the little “<…>” icon in the menubar showed “Connect” not “Disconnect” as the available menu command and the outbound emails all queued up but unable to be sent due to computer having been offline, all said IP Address changed from 70.19.20.210 to {empty space here} between 4/25/2009 3:14:13 PM and 4/25/2009 3:44:13 PM. and so forth.

I pick “Connect” from the menu and it very quickly negotiates a new IP address for itself.

What setting, and where, controlls whether or not it keeps making the attempt to get a new PPPoE connection as opposed to shrugging and deciding to wait until I show up and make the connection manually? Whenever I’ve lost a connection when I was right there working on the machine, my regular box goes into a perpetual loop of attempting to connect, tossing up a message informing me that a PPPoE server could not be found, trying again, etc. Why would it not have done that until it succeeded in making the connection? What would be making the attempt-cycle die out?