I run a free website and every year I do a one week fund raising for the costs. I don't have customers but a more or less dedicated community (some people are around for years, others come and go). The community always exceeds the amount I ask for.
This is a fantastic idea. "Hey, you guys obviously get a kick out of my website. Not asking for much - just enough that I can keep the site running and still awesome." I'd definitely pitch in $20 a year to a site that has entertained me for years.
The most immediate example that comes to mind is Wikipedia.
It works every time I see a site like mine try it. People are attached to the site over the years plus I am fully open about all the costs and expenses. The yearly amount is less than 20% of typical monthly income though, it is just hobbyists financing one part of their hobby. I don't think you could finance an actual job through this. But I think labour of love creates better websites than money-oriented endeavours anyways.
The key is making it very focused and short-time. People won't engage if you have a random donate button (I do, zero donations over 3 years). People love immediate motivation to participate in a common fundraising I guess.