I had only known "repair" to mean "to fix" or "to renew." Yet, I read an article this morning where the woman was going to "repair to her porch."

I looked it up, and sure enough there is a definition that says:

To betake oneself; go: repair to the dining room.
To go frequently or habitually: repairs to the restaurant every week.

Have you seen it used that way?

I've sertainly seen it used in that way plenty of times. It is rather old-fashioned, if not archaic. I doubt that anyone would use it in conversation these days unless they were deliberately trying to sound old-fashioned.

It's rather like someone talking about the "withdrawing room" in their house.

I agree with arnie. Though I've heard it. In American English it has a quaint, old-fashioned flavor to it. Like asking the gentlemen to retire to the library for port and cigars after a fancy dinner.

How do the two senses relate?

Two different words of different origins: to repair 'to restore' < Old French reparer < Latin reparo 'to get, acquire, or procure again; to recover, retrieve; to restore, repair, renew' (reparare) and to repair 'to betake oneself, to go' < Old French repairer < Late Latin repatrio 'to return to one's country' (i.e., to repatriate).

For some reason I've heard it quite a bit. Maybe we're still in the eightenth century here in Oregon. Or is it the eighth?

It's used still in England by old-fashioned or pedantic people (which is why I sometimes use it).

If I felt so inclined, I might well say, "Let us repair to a local hostelry" when I'm with another pedant (such as Oscar) knowing full well that he would appreciate the deliberate and accurate use of an uncommon term.

Funny, because this use was in an advice column (similar to Dear Abby) in our local newspaper. I wouldn't have expected a pedantic term there.

As has been mentioned more than once, there are several words in common use in the USA that have become uncommon or even obselete in the UK.

Gotten is one example (and I am sad it's gone from UK English since we have no comfortable alternative). Maybe repair in the sense we are discussing is actually more common in some parts of the US than in the UK.

Maybe repair in the sense we are discussing is actually more common in some parts of the US than in the UK.

Maybe in some parts, but not around here. I had never heard it used that way before.