usually with dsl it kicks you after about 72 hrs in the uk ... and 24 in duracells case
you could set it to auto connect when the line drops im sure there will be a tool for adsl i had one for dialup modem but i never needed look for one with adsl to use ... as i always re-connected it myself after 3 days anyhow
my router takes care of the connection and re-connection automatically now so no need to even have this machine on at all for access via the other machine which is good when it comes to maintaining or rebooting mine
sure you dont really need a router for 1 pc but they do reconnect themselves once set with no messing around
also like i said above it adds an extra layer of protection with the hardware firewall built in to the router which is always a good idea
you also have the option to add an extra machine at a later date
I find extra net ports a bonus when mates need their computers fixing i dont have to disconnect mine to use the net on theirs messing around installing adsl modem drivers and installing the modem on theirs then plugging it all back in on mine when ive finished ...now i just hook in with a spare ethernet cable and its connected to the net instantly