Unless You Pushed the Power Button On The DSL Modem...
...it should not turn off.. Was the modem's power button OFF? If so, there is nothing that can do such a thing other than someone physically pushing the button..
On the other hand, if the power button was ON and the modem was OFF, I'll ask you how you determined the modem to be OFF.. ?
Instead, as was mentioned by the other poster, if the computer went to "Sleep", it's common to lose an internet connection because of general operating system ineptitude.. If that's the case, then the modem didn't actually go OFF but instead the computer simply had problems recognizing the internet or its internal IP address.. A computer restart usually fixes such issues as it allows the computer to restart drivers, etc. and re-recognize the connection again..
Hope this helps.
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