are you 100% the modem was off line
next time it happens
first check where they modem is really offline
ie take a look at
http://192.168.100.1
how are you routing the network
as after seeing weather modem is operational or not I would start looking at router next
as if its just a small crap domestic router it proberly just running out of memory
what were you doing on network at the time of the loss of net
you were running bitorrent by any chance were you ?
that's great for killing crap routers