Im going to go ahead and assume you're running windows XP.
Something you can try,
Go into control panel > system > click on hardware tab > click on device manager > expand the modem tree > right click on your modem and click on properties.
Once in properties, click on the power management tab and untick 'Allow this device to bring the computer out of standby'.
It might be different for you.
You arent online using dialup at the same time you're trying to go into standby are you?