I'm going to answer the first part of my own question.
After upgrading my iPod Touch to iOS 5, Location Services started working again. Not only did it start working, it's showing the location as a point in the street in front of the house.
1) The location I manually submitted to Skyhook in 2009 was in the street farther south, by the mailbox, so the old data point is not being used. Not suprised since I have no reason to believe that Apple went back to Skyhook. A visit to Skyhook's website verified that this point has not changed.
2) The location that Apple started using last year was a point on the main highway 1/2 mile east of here.
So somehow Apple has independently obtained new data about my wifi location. It's possible that during a recent party, somebody with an iPhone had connected to my Wifi and that data was sent back to Apple. It's also possible that a Wifi data collection vehicle drove down this road. It's very rural with only three homes on a one mile stretch, so although possible it's difficult to believe.
It was my previous understanding that Apple started requiring that devices be within range of several Wifi signals to improve Location Services accuracy. Being in a rural location, it's nearly impossible for my iPod to pick up any Wifi signal other than my own. With Skyhook, this was never an issue.
However, iOS 5 seems to heavily depend on Location Services so maybe they've changed something critical to how it functions in order to improve accuracy without requiring multiple Wifi signals.
I'm going to accept my own answer. If anyone has a better answer to my original question, I'll consider accepting that instead.
From my own experience Internet Sharing is not, and has never been, as reliable as it should. Connection coming back and forth is a usual behavior of the service, heavily depending on the usage of the machine which is sharing the internet connection.
Apparently, updating to 10.7.4 makes things even worse.
Best Answer
It seems that you can need wifi on (but not necessarily configured) in order to get location, Core Location works using skyhook and will not function without wifi on. This is not well documented by Apple but this StackOverflow conversation covers it.
According to the above, you should be able to turn on Wifi, wait for a location fix and then turn it off. If that doesn't work look into WhereAmI, this project allows command line access to CoreLocation and you should be able to script it and wifi to turn on once in a while, log your location and then turn wifi off.