According to my notes from when I have done this before:
Q. How do I bake or fix the pose to the object? A. Pose the model and then switch to Object mode. Select the model (not the armature) or shift select all the parts of the object if it isn't one single mesh. Next, add a new modifier and choose "Armature". Make sure that the armature is moved to the top of the stack and in the Object dropdown menu, select the armature that you created and then press apply.
So the problem that I am having is that I have followed those directions exactly, but then when I delete my armature, my pose resets and I lose the pose. It doesn't seem that it baked it at all.
What is going on? How do I delete an armature but keep the baked pose?