Is it possible that my starter won't convert from WW to AP?

Have you tried feeding it half whole wheat and half ap? My starter has a hard time if I just feed it all ap, I generally also use a little whole wheat. Perhaps if you did half and half a couple times and then just move to mostly ap.

How do you quantify the happiness of the starter?  AP starter won't be as spectacular as WW one, it will likely ferment slower and won't rise as much, but this "your starter must triple" thing is a myth anyway.  If you want your starter to look a bit more lively adding a pinch of whole rye (5% or so) usually helps. 

Mike

What do you mean when you say the starter doesn't like its new diet?  Is it not rising well?  What about the flavor?

In general, whole grain flours absorb more liquid than refined flours.  So, if you have settled on a whole grain feeding regimen that gives your starter a nice feel with whole grain flours, chances are the starter is too wet when you use the same feeding regimen with refined flour.

White flour will rise better than whole grain.  I think we have a few centuries of people complaining that their whole grain breads aren't as fluffy as white breads to back that up.   White flour will also usually rise more quickly than whole grain flour.

However, if your starter is now quite liquid, it may not have the physical strength to hold the gases it produces  to let it rise.  Many people mix 1 cup of water to 1 cup of flour.  This makes a starter that has a hydration between 166 and 250% depending on how the flour is measured.  I find that mix to be too weak to rise well.   And to have other problems.  It might work well with thirstier whole grain flours, but most of the emails I get from people with starter problems use that sort of mix.

I recommend a thicker starter to sourdough beginners.  1 part of water to 1 part of flour by weight, and to feed twice a day.   It is more predictable, it doesn't need to be fed as often(combining 1 cup of water to 1 cup of flour with once a day feedings leads to starter starvation and maintenance issues in my experience - this thinner starter should be fed more than twice a  day).  If you weigh ingredients, it's easy.  To 100 grams of starter add 50 grams of water and 50 grams of flour.

If you don't weigh ingredients, things get trickier.  A cup of flour can vary a lot depending on how you measure flour.  However, I mix 1/2 cup of starter with 1/4 cup of water and whisk it.  Then I add 1/2 cup of flour when the flour is sifted before measurement or 3/8 cup of flour if the flour is just scooped from the bag.

My own observations...  with a starter at 100% hydration is that if it won't double itself between feedings, it has little chance of doubling the size of your bread.  With a starter mixed with 1 cup of water and 1 cup of flour all bets are off - you have no really good telltale to gauge its activity level.  Which is another reason I suggest the thicker starter.

Mike