"how do you... keep going when you stop caring"
Continuing to work on something, when you do not enjoy it and you're not going to get paid, would be insane.
The problem with this is that there are always periods where you have to do stuff which you don't enjoy - and if one isn't careful in those situations, the "I don't care anymore" feeling can be generated by a wrong impression, e.g. that the current (necessary) tasks are not connected to the project anymore.
Translated this means: creating a [mod] [game] etc. is 5% fun, the other part is hard work. (figures just to show the relation - no real data)
So if you find yourself in the situation like this:
1) Do I enjoy writing a quest? -> Yes
2) Do I enjoy program a quest system? -> No
You shouldn't answer this one: "Do I enjoy working on the project?" while working on your "quest system" (which you don't enjoy :D). Instead you should get some distance to both 1) & 2) and e.g. re-evaluate the overall achievements.
Shihonage already mentioned that - look at old screencaptures, screenshots, design iterations etc. and FEEL your process. Make it clear for yourself what has been done, then decide if you still care or not.
And as we are in the "amateur league" you also have to take into account what you learned so far.
Sure, it is tempting to "just throw away everything and start something new" - but you eventually get to the same point with your new toy, too.
Constant feedback and having a community of people interested behind you is a must. Have a forum, a Facecbook group, release screenshots, gameplay videos.Get positive feedback so that if you feel like going on.
My opinion regarding that one: It can work, but it can horribly bite back. If you rely on the constant feedback too much and it is gone (people change - we are talking about time periods spanning years), it can harm your motiviation and / or the motivation of your team.
So I factor that one out for the "early stages" - made that mistake once. People with an outside view can be helpful, but they can also make you loose your focus (e.g. "Feature XY is a must" "Oh, you are right... *worksonnewfeatureandloosesfocus*").
For everything there is the right time, and constant feedback is IMO only helpful if you are prepared for that (project-wise). While moving a lot of code it is sure not helpful to get distracted by a totally new feature. But when you are in concept review process (Beta testing!) it can be a powerful help.
So far, that's my condensed (lol) view about that - with the background that I'm working since 2006 on 2 large scaled projects (FIFE & Zero), so for a little mod it sure can be different, but the principle stays IMO the same. (project management stuff, organisation, team dynamics blabla...)