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Well on a permanent pier my Vixen Atlux does this rather well - you simply turn it off when you are finished and cover it. So long as you don't turn it off during a fast slew (who would do that?) - it is supposed to remember its exact set up.
With good polar alignment I have found it is pretty accurate on power on - say within a few arc minute of its (singular) alignment star. So I have say aligned on Achernar and at 3am switched things off. On a clear day a week later, home early I switch things on at 4pm (it gets dark around 8:30pm) and slew to Achernar or Canopus and its very close to dead centre. I generally sync on it again and there is my alignment process done.
For the next 3-4 hours I can periodically monitor the drift if any in this star to confirm the accuracy of my polar alignment.
And no I wouldn't advise trying it on anything within 50 degrees of the Sun.
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