Can I slow cook in short intervals? I'm making tonkotsu ramen broth, cooked over twelve hours (some people cook it even longer). I'd rather not leave my gas stove on overnight, so I'm wondering whether the same effect - breaking down collagen in meat and bones - can be achieved by cooking the broth in intervals of four hours over a few days. The broth would be refrigerated in between. It's not ideal, but I would think that the same collagen-gelatin conversion would take place... right? Is there a downside to trying to slow cook in short intervals? If this were braising meat, the meat would dry more, of course. But since we're mostly talking liquid, bones and fat, the change in temperature (and congealing then liquifying of fats and collagen) shouldn't make a big difference right?
The obvious downside is safety: each time you go through a heating and cooling cycle, your food will spend time in the danger zone. It's hard to guess exactly how long, but if it's a large volume and it takes an hour to cool to 40F and 15 minutes to heat back up to 140F, and you use the conservative end of the safe time range (2 hours) you might have a problem. You could partially alleviate this by using an ice bath to chill faster.

If you can avoid the safety issue, in terms of the resulting broth, it sounds fine though.

That said, slow cookers are awesome, they're not too expensive, and that'd solve your problem with much less effort.