I think the problem is that people associate low cost to low quality.
The instinctive reaction will not be to your generosity but that the price of the product(service) doesn't inspire confidence in it.
There are several studies, I just don't know where to look for them now but we discussed them when a friend of mine was studying, about commitment and price point. That a higher price indeed makes people more likely to stick to it because it hurts them too much if they don't (financially).
I'm no strategist when it comes to fees (and I have set the membership in my own club on semi-annual basis) so I can't really say what effect a change would have. But to some people, the $1 price tag will be interpreted as you yourself do not think the training is worth more than $1.
It's horrible that one needs to resort to those kind of number juggling but I believe having a high price point and a "campaign"/discount might help. In other words keeping the paid price low but showing it as a heavily discounted higher price. Also consider doing some kind of package deals maybe, $5/class and 10 for $40 or similar.
This is the aspect I absolutely detest when it comes to running a (very small I might add, we're only 12 people incl. me the instructor) martial arts club in the middle of a metropolitan area, because one needs to play the numbers to make the price seem both serious [everybody knows that pros train with expensive teachers] and affordable.
People won't realise why you set the $1 price point, so they will often assume the worst; basically that you can't convince anyone to pay more.
If you were to stick with the $1/lesson pricing then maybe add some kind of value explanation/philosophy behind it and tie it in with the core values and traditions of your martial art as well.
PS. These are just my thoughts on the subject, we pay 450 USD/month in rent for a total of 12 hours training time (two 90 min sessions/week) in the dojo where we rent. These are just the things I've observed and considered for my own part, but needless to say with our low numbers (and the fact that they used to be lower) no year completely adds up but requires money from my own pocket to cover. Essentially I need to collect 24 membership fees per year to break even. Started up in the beginning of 2011 and this might be the year it happens.