I've been burned out like that, too.
I think the above is the perfect plan - just work on the program as if it was just a tool for yourself, add / fix the things you want, don't add / don't fix the things you think are not worth adding or fixing, etc, and let the community sort out the rest.
If someone wants to grapple with that server-side logoff, for example, (ie, by caching user credentials for the session and resending the authentication form when the server expires the cookie), they can, the source code is out there (and you are even maintaining it, keeping it free of bugs that bother you, etc), adding things is simple. Let them fork the project and go on their own. When Valve break that by adding a captcha, that's going to be their problem, not yours.
Same triply so for support - you have the FAQ, that's 99% of the value you are going to get. Answering the same (wrong) questions over and over and over and over and over eats a heck of a lot of time, and the kicker is - it doesn't help. It's just way too inefficient to make any difference.
IdleMaster is a great piece of software that is adding quite a lot of value to the Steam accounts of many, many people. Don't let the byproduct of its popularity - clueless users asking same dumb questions and demanding things - upset you, it's just something that happens, the sun rises every morning and popular programs get their dose of clueless users. It's ok to just ignore them. /brofist