We have had the same problem with Rent-A-Mum. They never seem to have people available, the girls tend to be quite young and while sweet, don't appear to be highly trained nannies.
The organisation is terrible, waiting for a nanny to arrive at 10am one morning I received a phone call from Shirley at 10.10am to say that she had slept in and hadn't given the nanny the address yet!
On two occassions, I have booked through them only to have them cancel at the last minute and one nanny we had told us pleasantly when we got home that our 2yr old toddler had "put himself to bed while she was watching TV".
Yes, some competition is definately needed. I am trying Annerly Nannies annerley.com.hk - hopefully this is better!