It happens - for all the reasons Kate mentioned and then some; within our own industry is especially frustrating but it reflects poorly on the VA who offered you such a meager rate and not on you at all.
You know what your services are worth and Kate's suggestion of using this situation as an opportunity to educate your potential client a bit is something I've often done myself.
If it's really put you in a place of feeling like you want to throw in the towel - try posting a gig (even on Craigslist) and ask for writing samples and rates - you'll be AMAZED at the poor quality of results you receive (and yes, even from high priced American VAs) and perhaps it will bolster your own confidence. I did this myself, early on in my practice to help me better 'rate' my skills and talents and fine tune my rates.
In the end I rest assured that I charge far less than other service providers who are offering very low quality returns.
The potential clients (VAs or not) learn the hard way - not much we can do about that
Hang in there!