Is there benefit to continued stirring/agitation of starter once a krausen has started to develop? That is, once the yeast has entered into anaerobic metabolism, I am wondering if it still helpful to encourage air-exchange.
Your starter will benefit by continuos aeration until all of the fermentables are used up.
I give mine a good shake every time I walk by it. This is probably once every couple of hours when I am home. Be careful, some starters can foam up when you swirl them. Do a slow shake first to make sure you don’t lose any yeast out of the top. I usually use 400 ml of starter in 1000 ml flasks when I make a starter.
I would second this. I just had a starter of Wyeast 1056 foam out of a growler and it looks like I lost some nice, healthy yeast.