River Cottage

Hello, all ideas welcome because I'm flummoxed about my starter.

Started off with 250g warm water + 150g brown flour.

48 hours later, showed mild-vigorous activity, so repeated the above but with white flour. (And changed my tiny pot for a big yoghurt pot)

A week later, despite daily stirring to encourage more wild yeast being captured, nothing. There is just separation - a layer or liquid on the top, and no bubbling.

Has it died? Can cheap flour (the white flour was cheap!) killed it? Or is it just lazy? There is some activity, the tight lid keeps popping off and there is a distinct lovely sourness to it but what's happening?....

Does one use the same bag of flour for the entire process? Do starters die?

I am reluctant to dump it because it's only my second (but first successful!) starter, and have no idea how to proceed.

Do I keep feeding it without removing a part and replacing it? Or start feeding it (removing a part) and storing it in the fridge?