When tillering a bow, should you unstring it every time you have to remove more wood?

No, once the limbs are bending enough for a string, it can be left on.  Usually at this stage you'll want to use a tillering string.  A tillering string is longer and thicker than the string that will eventually be on the bow for shooting.  It's longer so you can adjust it to however long the bow is that you're working on.  And it's thicker and stronger because the bow will be at a heavier draw weight than it will be when it's finished.

I have one tillering string that I've used for every bow I've made.  And when a bow is done, I make a permanent string for it.

Obviously if the tips of the bow need any further work, the string will need to be taken off for that.

Thanks  :)

I generally take the string off.