you're welcome, thank you for your kind words!
you can definitely take a break, but there's different methods for doing so. keep in mind that when you stop cycling and let time flow naturally, you break your cycle and thus will have to change your boxes day. so if you decide to take a break for however long, when you do play that town again you'll need to TT indefinitely until another villager is in boxes and then resume your cycling from there. this is always what i do, because usually when i stop cycling it's because i get distracted or caught up with other things, and also because i have no patience whatsoever.
the other option is writing down whatever day you stopped cycling (it's always a good idea to stop on your boxes day, that way it's easy to remember which day you need to go back to) and TT back to that day whenever you're ready to begin cycling again. that way you can just pick up exactly where you left off. my brain isn't fully functional right now (very overworked and sleep deprived at the moment, so i apologize) so i may be wrong on that, especially since i never keep track of anything and don't use this particular method myself. but as long as you don't load your game on any day other than the last one you played, you should be fine. good luck! c:
okay, so basically, when you use the method in this guide to do your cycling, you'll be TT'ing between three different dates, depending on what your "boxes day" is. if your boxes day is 4/6/16, you'd be TT'ing back to 4/1/15, then to 4/1/16, and then back to 4/6/16 again. if you load up your cycling town on any day other than those three dates, you'll have accidentally broken that cycle and messed up. from that point on, you'd have to TT indefinitely until you can get a new villager into boxes, because the foolproof method only works if you have a villager in boxes.
say you decided to stop cycling for a little while. your cycling town's date is set at 4/6/16, so you write that date down somewhere so you don't forget it, and then you go on with your life. when you want to begin cycling again, your town will be several days, weeks, or months ahead, depending on how long your break was. if you were to load up the town without TT'ing, you'd probably have only 8 villagers and no one in boxes, because you would've broken your cycle. so if you TT back to 4/6/16 before you load up your town, the game doesn't realize you've been gone at all, and you should be able to resume cycling right away without any problems.
whenever i've stopped cycling, it's usually been because i got busy and stopped suddenly, so i wasn't planning on taking a break. if you don't write down or remember the date your town was on when you stopped, you'll just need to load your game at whatever date it's on and TT day by day until you find another mover. i hope this cleared up what you were confused about!