You have a bug they want to fix or a feature they want to add and the author/maintainer is not doing it fast enough? Fork away! Submit a pull request! Oh, you don't have the skills/time to do that? Wow, that's too bad. Offer to pay the author! Post a message to the project list or bug reporting tool offering to pay someone to do it for you. Oh, you want it for free? Immediately? You built critical infrastructure around a tool you don't understand and don't have the skills or resources to maintain? You're a parasite, and can be safely muted and ignored.
This is the important bit: If you're afraid the person maintaining your key infrastructure for free might suddenly stop doing that, just take some time to send them a nice note thanking them. Periodically getting one of those in your inbox is remarkably effective in maintaining passion for a project. Find a way to give them a gift. Do they have Venmo/Patreon/Amazon wish list? Use it. Are you a developer or do you employ some? Fix a bug. Say nice things about them in social media. Offer to help pay for the resources to host the project. Send them an effing Starbuck's card with your sincere thanks.