For me, the last day I didn't program or worked in anyway on my project was around August 15h, 2017 according to my Github history.
I think everyone is made up differently, so this will vary.
my 0.2 cents is that you should keep the brain and body happy. Try to take productive breaks is what I try to live by.
Very nicely put, Kev! Indeed, this is a very personal affair.
For me it works to do several intensive months of work and then do an extended period of a month or so when I focus only on Big Picture stuff - helps me a lot to clarify direction and come up with fresh ideas which to pursue intensively again afterward. But this is also related to my natural rhythm for work.
As @kev stated, probably the most important thing is your mental and physical health.
I observed that it's really hard for me to recover and get back into my productive mood if I take a week or more off. That is why I like to work every day at least 2 hours, be it a personal project or client work, anything really. In the same time: I try not to push too hard myself and avoid as much as possible working for more than 8 hours a day.
Also, as @maringerov mentions, I also practice taking off a week once or twice a year when I concentrate on reviewing the last few months and defining my next goals. If it weren't for these, I probably wouldn't be able to motivate myself to learn and work everyday.
I try to take breaks by diversifying the tasks I do as much as possible. If I'm coding for a couple of hours and I get bored, I change to designing, or marketing, or project planning.
And sometimes it's good to take a break from your computer for a couple of days, go out and just talk to people or think about your project.
But as sais, everyone's different. So just go with your feeling and do what comes naturally. There's a reason we won't work for a boss :)
How do you define "taking a break"? One day without committing any code?
I define it as my Apple Watch telling me I should get up for a while! :D Nah, just kidding, that's a good question. I think that @Sachertorte was thinking anything above a single day off.