I had a 30# terrier/chihuahua mix who had the same problem. It started when she was maybe 10, and continued until she died at 14 1/2. She'd lose at least 2 a year for no obvious reason, like getting a nail hooked on something. I would notice a nail suddenly looking extra long, or notice her licking a lot, and upon closer inspection see that the shell of the nail had mostly detached from the quick. When it would finally come off, it would bleed like mad until she licked it into submission.
Her nails were also an odd texture inside -- ie, when they were trimmed and you could see the cut end, they were almost crumbly looking. I never got a diagnosis, but I am pretty certain it was some type of fungal infection. I could have spent some money delving into the cause and putting her on some type of medication for life, but it was not affecting her health otherwise. Her blood work was always perfect. The biggest issue was the bleeding when the nail came off, but she'd clean that up for me too.
So, I would pursue the idea that it's a fungal infection for a start. Save the nail if another falls off and take it to your vet. You might even be able to mail the nail to a vet school - there is a great one at Univ. of Mo in Columbia.
Links to Univ of Mo:
Univ of Mo Vet School
Diagnostic procedures available:
Information and Services
You could contact them via email or phone first to see if they could help if you sent a specimen.
Good luck, and please report back if you find any answers.