Finally questions I know some answers to!
First, you've done well to see a neurologist and a pulmonologist. However, are either of them sleep specialists?
If you go to a really good sleep lab, you'll usually get good data to at least have an idea of what is going on...
You could ask them to monitor something called End Tidal CO2, which is often abbreviated ETCO2.
I hate to burst the "she'll outgrow it" bubble, but we've heard that line for almost 5 years now, and finally have a doctor that admitted that our son will likely carry the same diagnosis to his grave that was assigned to him at a mere 5 months old. That is: Unresolved Primary Central Sleep Apnea of Infancy. Now, some kids do outgrow it, but you can't get complacent with it, because as soon as you do they regress and things get really rough again...
Keep us posted..I'm still working on some information about VSDs and apnea links!