Can I obtain a multi-entry re-entry permit via drive-through at Phuket immigration with a retirement visa?

You can’t do it at the drive through. If more convenient you can also get a re-entry permit at the Patong office or the Blue Tree office.

@Stuart ********

do you know if that drive thru at the Phuket office sells re-entry permits

I don't think you can. You have to go to the "standard" office to apply for a re-entry permit. But let's see what other members in Phuket say.

Usually, drive-through counters don't handle something that deals with an actual stamp on your passport.

Remember, a re-entry permit is valid only until the current stamp is up, regardless you are on an entry stamp from an actual visa or an extension.