The Django Rest Framework library has taken this very approach [1] offering both corporate and individual monthly subscriptions which is then used to fund development. It appears to be quite successful in that it's allowed the lead developer to work on the project full time (at a salary of £50k [2]).

[1] https://fund.django-rest-framework.org/topics/funding/

[2] http://www.encode.io/reports/february-2017