I don’t think quitting is an option. There always is more to know and you are never “done”. Even from a practical standpoint: If you are a curious person you probably still sometimes look up words in the dictionary, words in your native tongue that is. English isn’t my first language (surprise surprise) but I’ve been speaking English almost exclusively for roughly 8 years, and I still have some big issues and bad habits I should take care of. I’d also be utterly lost without the spell-checker function of Firefox, but I think part of that is due to the fact that I’ve learned most of it by immersion. I believe that if you are in it, you are in it for life. If you intend to use it you will always keep learning. I don’t think anyone knows all the words of any “living” language.

Unless you actively avoid looking at things written in Japanese, you never give up “learning” it. Even if you decide to stop “actively studying”, every time you read or listen to Japanese, you’re getting ever so slightly better ;)

When you see no progress with your work?

Nope. You’re just plateauing. If you’re seeing little progress, mix things up a bit, study differently.

When is Japanese going to pay off?

When your knowledge of Japanese positively impacts your life in any way. Even if you’re just able to read one ingredient on the back of a packet of something or other – if you hadn’t known the Japanese you knew, you’d have less idea what you were buying ;) If you see some Japanese and go “Hey, I know what that means, awesome!”, your Japanese has improved your mood just the tiniest bit, and I’d say that was “paying off”.

When you learn to play the guitar you have tangible results in months.

Firstly, you have tangible results in *anything* if you’ve been learning for months. Also, it depends how much you’ve practised. If you’ve worked on your Japanese 1 hour a day for 3 months, you’ll be far better at *that* than you would if you’d only been messing around on guitar here and there one day a week for 3 months.

When you study Japanese, identifying a full youtube title of a video is the closest to ‘mastery’ you’re ever going to get.

Uh, what? That’s not even nearly true. Think how many people who have learned Japanese can use it day in, day out conducting business in the actual country with actual native speakers. I’d say that was closer to “mastery” than reading a YouTube title :P

I see blog posts that I can understand the gist of, but there will always be Kanji that evade me.

As is the same with most people who haven’t done KanKen 1 ;)

No matter how many Kanji you know, you never will know enough, unless you’re Asian.

How many is “enough”? You realise Asian people are humans, just like you and me? They don’t have special kanji-learning genes – if they can learn so many, why can’t we? Remember that native Japanese people both don’t know all kanji *and* regularly forget ones they know. As Zeldaskitten said, I certainly don’t know every English word and I’m native.

What would be the ultimate warning sign that you ought to quit?

If you’re really resenting it or it’s negatively impacting your life in some other way. If you have to choose between spending time on Japanese and spending it on something really important that actually needs done, put Japanese on the backburner, don’t just give up outright – there will be time for it again later.

The frick is 畳?

It’s “tatami”, as in the mats that are found as flooring in Japanese homes. It’s in the Jouyou, so it’s not exactly rare :P

While looking at no dictionaries whatsoever

Then look at a dictionary! If that’s a word you want to learn, learn it, then next time you see it, you should be able to recall it… possibly. That’s how learning works! :D

Just because you feel you suck at Japanese now, doesn’t mean you’ll suck this much forever. If you keep at it, you’ll suck a little less each day. Eventually, you’ll suck so little, it won’t be that noticeable ;)

I would also recommend downloading one of the Rikai tools, so you can hover over Japanese and get a translation.

http://www.textfugu.com/bb/topic/japanese-learning-resources/

It’s listed under Browser Extensions.

I know in Spanish class, my teacher brought up an interesting point. She was explaining why she used one tense instead of another in a sentence. The sentence was “I study Spanish,” and she used that tense because she is still learning Spanish, even though it’s her own language.

Now that made me think. I’m still learning English. For example, I didn’t know the word “extirpate” until yesterday. I never heard of the word “abnegation” until I watched Divergent. I remember my friend learned that the word “zeroth” is in fact a word in Physics class with the 0th law of Thermodynamics.

If you’re a native English speaker, chances are that there’s still a myriad of vocab words you could learn. Even if you know argosies upon argosies of vocab words, you could still learn to understand Shakespeare’s plays and how to talk that way.

Once you start studying a language, as long as you keep in contact with the language, you don’t really “stop” learning it. Sure, you might reach a day where your efforts don’t help you as much as they did in the beginning, and you might have already accomplished your initial goal for starting to learn Japanese, but that doesn’t mean you should stop.

@Jack Kagan: Yup, you can have 0-th, n-th, k-th, r-th, even n-plus-one-th.