The reason I would close them is that it very cheap to do so after a sudden increase in the stock price, and if the stock falls back I can write the same put again.

1. It may be cheap to do so, but it still costs you some money. And since the stock went up so much, it's almost all time premium you are buying.
2. Yes, you can write the same put again, But because of the elapsed time (between the stock having gone way up, and then falling back down again), you will receive less time premium the second time around. And besides, you CAN sell the same put again WITHOUT buying back the old one! I just looked at the history of a particular put (not BRKB) I sold in Sep '22, it is a Jan '25 put, and I sold some in Sep '22 ($21.75 each), sold some more in Nov '22 ($20.80 each), and twice more in Dec '22 (first at $22.55 each, and then after a big drop at $26.95 each). Today those puts are each trading at $0.25, and I still can't think of any reason to buy them back. Of course, unless I want to book the capital gain in '24 instead of in '25 when they will very likely expire worthless. If I want the gain in '24, I would buy them back in December.