A lot of people will recommend the obvious chemistry solution - if you have a caked on base, it needs an acid.
From working with PBW, I find that isn't always the case. You need to give your PBW what you'd give your lady. More, hotter, longer.

Rinse with a larger volume of water than the PBW used. It needs to be at a hotter temperature as well. And rinse longer. Much longer. When you think you've rinsed enough, you're probably halfway done. That's just general advise for PBW.
When you get the "staining" or caked on residue, acid isn't always the immediate solution. Attempting to lessen the problem by another PBW soak is often beneficial. Again, more, hotter, longer. Give it a good soak. Put on some heavy gloves & periodically go over it with a soft cloth rag. When you're done with the soak, rinse it. Immediately. More, hotter, longer. The very second you're done rinsing, then hit it with the acid.
This is actually a pretty common problem with carboy necks as well. It's been a while but from memory, I hit it with 70C PBW & rinse no lower than 90C. For a prolonged soak monitor the temp of the PBW. Don't let it crash. If you need to, do a PBW "decoction" to keep the temp up. Losing a few degrees isn't a big deal, but crashing it during the soak is one of the causes for that "stain" or residue.