Lose private house if switch GC?

So in order to buy my house I had to be a certain rank in my GC first. What I'm wondering is will I lose my house if I switch GC?

Sure will not lose it. I bought mine and the house has no any association with the GC. ^^;
It is just the prerequirement to be able to purchase a house.

- Purchasing Land
In order to purchase land, a character must first have attained level 50 in at least one class and also have earned the rank of second lieutenant in one of the Grand Companies.

yeah, keep in mind that if you switch your GC you will NOT lose your rank in THAT GC. So when you switch back, your rank is still the same.