I have a 4 year old IBM Thinkpad A21 running Mandriva 2006.1 and it is mostly good but the harddrive is always spinning down and up even when connected to AC Power.

I have tried using HDPARM to fix this but it has no effect.
Run:
# hdparm -S0 /dev/hda

/dev/hda:
setting standby to 0 (off)

Then only a few seconds later:
# hdparm -C /dev/hda

/dev/hda:
drive state is: standby

Shouldn't the drive stay active after hdparm -S0?

Yes, it should stay active after giving it -S0. This works fine on my system. Now as to the fix... I'm not really sure. I'm going to investigate what mechanism actually spins down the drive.

Good luck.

I have a 4 year old IBM Thinkpad A21 running Mandriva 2006.1 and it is mostly good but the harddrive is always spinning down and up even when connected to AC Power.

I have tried using HDPARM to fix this but it has no effect.
Run:
# hdparm -S0 /dev/hda

/dev/hda:
setting standby to 0 (off)

Then only a few seconds later:
# hdparm -C /dev/hda

/dev/hda:
drive state is: standby

Shouldn't the drive stay active after hdparm -S0?

Are your filesystems ext3? Jounalling filesystems write every few seconds.