I feel your pain. I just went through this not too long ago... without success. 
What I suggest out of hind sight is straight forward questions like "You don't seem to be getting this because I keep having to come back and re-train / fix your errors / etc, etc. What can I do differently when I'm training you so that it is easier for you to get?"
My employment theory is that no one should ever have to be fired. If they get fired it's the company's fault for not being able to hire, train or motivate effectively.
You may also try one of the online tests to help assess. Like learning style, or personality to determine her strengths and how she learns best.
Remember learning something new is directly coorelated to motivation to learn it. No matter how good the training, if they aren't motivated correctly they never will take time to learn. You may also find out what motivates her. Money, status, accomplishment, retaining her job 
That's my input.
I dont' really have much to offer except to say I think you are an excellent communicator and a wonderful person. Hang in there and keep on keeping on. I'll be praying something changes soon.
Sounds like a classic Adam & Shannon. His mind works quite similiar to your Betsy. He never understands why I don't "get" some things. I should just "know" how to do it. I used to be quite intimidated by husbands intelligence. Until I realized I am just as intelligent just at different things than he is.
Option 1:
She may be a verbal person. Not you saying it out loud but her saying it out loud she can hear herself.
Option 2:
Watch for BMIRS... Behavioral Manifestation of an Internal Response. Ex.-Confused expression, frustration expression.
Make note of the moment you notice the expression. What was she working on, what step was she trying to complete, etc.
Option 3:
Have her write what you say. This way she writes a map that she understands.
Hope maybe this will help...
Sorry to hear about the frustration! Can be hard to show something "simple" to someone who hasn't seen it before.
People can be like sponges, you soak it in until you reach a saturation point. Then nothing else can get in, and you drip out what you already have!
So often we struggle to learn something, and then later look back and ask, "why was that so hard?!?"
I agree with Matt - sometimes you've just hired the wrong person. (reference book, "Good to Great", success depends on having the right people on the right bus going to the right place. After a reasonable amount of time, she'd probably be relieved to hear, "this just isn't working out." Letting someone go so they can find the right job is often the most humane treatment! They want to be successful too.
We'll be praying for you!
Commenting by HaloScan
