I think you might really be asking about sustainability, not profitability (profit is what you have after all the bills are paid). It’s generally donation-based. I’m sure different communities will have different ways of soliciting donations.

EDIT: I’m no longer partial to the below. I much more like PrimalAnimist’s suggestions.

For larger, expensive instances, I’m partial to determining the cost of running a single user over some period of time (say, 5 years), and posting that little datum on the community info. Then, each user that donates that amount gets a badge reward. Users that pay double the minimum get a different badge, and so on. Cycle the badges every n years. Some users will have fancier badges, displaying a kindness for the poor and badgeless. Cultivate a culture of gratitude for those who support, and you won’t have to worry so much about not having enough.