Wow, I don't know if I've had someone so thoroughly check up on anything before posting here.
It could be mold. Since you are in a basement, mold is quite common. She could also have poor circulation.
The fact that it does not occur every night, or maybe for a whole week at a time really makes it a mystery.
I would suggest an alternative health care doctor, maybe a homeopathic doctor would have an answer. Some can determine what is wrong with their patient by just looking (no tests or prodding involved.) Some can also determine allergies that regular clinicians cannot. I would think it's a food allergy that isn't coming up from the tests that she had since it's such an uncommon occurrence.
If you do find out the cause of this, please do come back and let us know for others who might have the same problem. All my best!