Although I wonder if the break is really necessary. I have taken an intensive language course (10 weeks, full language immersion and homework from waking to sleeping every weekday), and the full brunt of the language skills I learned didn't hit me until ~2 months later, where I find myself understanding the learned language constructs intuitively without deliberate analysis. It may just be that it takes time for one's subconscious to fully integrate the newly learned material, especially for complicated and non-intuitive subjects such as language, as opposed to any special effect from taking a rest from it. Another aspect is that learned material have an expiration date or a half life, so that if I take too long of a break, it would disappear as opposed to being strengthened. This is where spaced repetition software comes in handy for me, especially for rarely used vocabulary (which are often the most important words in a sentence, and the lack of understanding of would change the meaning of the sentence entirely).
Anecdotally my experience would suggest that they are important.
As someone living in one European country where English is less frequently spoken and occasionally traveling for work to others where English is more prevalent, I always felt that I could notice a real improvement in my second language upon returning "home" after speaking English for three or four days.
Incidentally, those same breaks usually resulted in improvements in rock- climbing (which are a bit easier to measure objectively because of the grading system), but I tended to attribute that to a full recovery / perhaps I was over-training.
Thinking about it now, maybe it's odd that I always accepted that the stenuous physical activities naturally needed a recovery period while assuming that I could just keep hammering at the mentally taxing skills day after day.
