Bill,
It sounds like you have not made the correct adjustment there should be no drift once the mount is correclty adjusted...unless you are referring to the slow E-W oscillations due to PEC.
What I do is :
Get your mount level - not to critical but get close.
Get your mount to point S using a compass - remember to offset for Magnetic VARIATION in your area - you need to point TRUE S not MAG S.
Set the ALT scale on your mount to match your LATITUDE.
Now slew to a star on the Meridian in the N (or close) and adjust youe AZ settings to remove drift.
Finally do the ALT setting using a start in the E.
This might help too:
http://www.petesastrophotography.com...alignment.html