I'm surprized no one has answered this thread yet
The quick and easy answer is, I don't 100% know. But not knowing for sure doesn't mean I can't have an opinion.
I have to generalize to answer...
First, it's usually individuals not 'schools' who teach for no money. minimum-profit schools charging operating costs are all over, some advertise, some only have a website, many just have a sign outside. word of mouth gets you to the teachers who teach privately. many have their own policies -a typical one being, if you don't like their policy, then leave. lol Most private teachers don't accept kids (less than 17). some have a pre-shodan requirement. (ie won't teach beginners). some only teach weapons, some never.
specific case:
The current school I'm at is a first I've seen that is operated by 2 equal skilled sensei which work full time elsewhere and alternate teaching...it's a great setup and allows them to have the dojo open every day of the week. The rates per month (not per class), no contract policy, and giving keys at green belt level tells me it is non-profit and as enjoyment. very practicle solution, but most teachers are so independant on how to run things, that the differences would end up as arguement. They allow each other to teach as individuls, while keeping to the style's framework and spirit. Their personality and easy going way are the main reason for attracting and keeping members. word of mouth gets them about 1 new student every 3-6 months or so. with a total class size of about 25... and an average class size on any particular night of about 10.
There are Sensei that can give more solid reasoning without guess or generalizing like I have...also ther are some members here that have done quite a bit of homework to find what they were looking for. hope they answer your thread