Screen Won't Come Back On After Inactivity

I duly used the Search function before posting, but while there are numerous threads in the archives about screens going blank, I didn't find any that matched my precise variant of this issue.

I have a Lenovo ThinkPad T61p running XP Pro. At times following periods of inactivity, the (built-in LCD) monitor will fail to come back on when I try to use the computer again. A short time after I stop typing, the XP screensaver will come on, as usual. Then a bit later, the screen will power off, again as expected.

The problem is that sometimes the monitor won't come back on again when I wish to resume work and hit Return to get to the login screen. In order to regain use of the computer, I'll have to hold down the power button, power off, and do a fresh boot.

Please note that unlike the cases mentioned in previous threads, this never happens at random while the machine is actively in use; nor does it ever happen in conjunction with boot-up. There's no additional video weirdness whatsoever. I haven't changed any power or screensaver settings in the 3 months or so that I've had this machine.

Any advice would be appreciated.