As DXoverDY said, when the computer goes to sleep, everything turns off except for the ram, which is fed just enough power to keep your active applications alive. The problem with keeping Aim online is that the airport card (for wireless internet) and the cable hubs (for direct ethernet internet) are both shut down to conserve power. There is no way to get around this. Its just the nature of sleep.
The only suggestion I could give you really is, if you really need aim to stay on, you can shut your screen off by bringing the brightness all the way down, and turn all the energy saving settings on. Also make sure all the components are turned off (ie. airport and bluetooth) and that nothing is connected to the computer through cable lines (except the ethernet cable if thats where you get internet from). Thats almost like sleep, but its still going to use up substantially more power then actually putting it to sleep.