how long is the computer asleep for? is it instant? usually an apple will restart automatically if there is a power failure. your computer could have a number of issues wrong with it. try putting it to sleep plugged in without the battery in it... see if it does it. also, try the usual... reset the PRAM by holding down +Option+P+R on reboot and hold it until the computer chimes, not once but three times. also, then when the computer is off, reset the firmware, by holding down the power button until the light flashes and the computer emits a long tone. If none of those issues fix it, you might have a problem with a dc board or logic board and need to get it replaced