Sounds like you need to pull your GPS power from a switched source so that the cradle power is removed when you shut the bike off. If your battery and charging system are in good shape, your GPS shouldn't be draining your battery to the point of faulty operation. Might want to get those checked.
If your GPS is still draining power when it's shut off and you want to keep the cradle hard wired, then maybe you just need to physically remove the GPS when not riding.