Looking at the their budget reports, about 2/3 of their funding comes from county, state, and federal sources.

I didn't trace the history back further to find out who was responsible for the cuts in the first place (although since the state has been responsible for the the biggest chunk of the funding, it's not hard to guess). However, with political leaders since 2009 at each of those levels of government supposedly being staunchly in favor of public healthcare spending, I wonder why they didn't restore these services?

The money is there. It was just used for overpriced courthouses, waterfront development projects, giant roads projects, bailouts, and stimulus projects. Instead of giving contractors stimulus dollars that often were used to hire foreign workers in circumvention of the rules, couldn't some of that have gone towards restoring public health funding?