The technique and product you use to do your initial twists for the twist-out will play a big role in how long you can preserve your twist-out. I say, the better defined your twist-out is at the beginning the longer you will most likely be able to preserve it. Additionally, the amount of moisture you expose your twist-out to will also determine how long you can preserve it. If you expose your hair, when it is in the twist-out style, to lots of moisture you will not be able to preserve it for long.
I searched YouTube and found some techniques used to preserve twists. You may have to try each technique to see what works for your hair texture, hair length and your routine. One may take longer than the others and each technique will give you slightly different looking twist-outs. So try them out to find which you like best. Remember, the more you practice the faster and better you'll become which means less time spent on your hair. Do not get frustrated the first few times, keep at it and you'll become a pro.
1) The Scrunchie Method (Video by Naptural85): You put your hair into a big bun (or several buns) for the night. Best on longer hair and will stretch out your hair the next morning. Seems to be the least time consuming. May not preserve your twist-out for too long before you have to re-twist.
2) The Banding Method (Video by Prettypr0f0und): You put your hair in sections and wrap bands around each section. Similar to the scrunchie method. I recommend using "ouchless" bands not rubber bands because rubber bands can snag hair. Also consider putting some oil on the bands you will be using. This method is also less time consuming on longer hair. Good for shorter hair since you have to put hair in sections. A variation is to use thread if you do not have bands. Will also give you some stretch the next day.
3)The Re-twisting Method (Video by Nikkimae2003): You re-twist your hair but in bigger twists. I think this is more time consuming especially if you have shorter hair. Plus, I prefer being able to preserve my twist-out without having to re-twist no matter how big the new twists are. A variation is putting the sections into big loose braids. Making the braids tight might give you a braid-out the next morning. Ooops! The re-twisting may not stretch out your hair the next day.
I hope this helps. If any of you have your own method of preserving your twist-out, different from what we have shown here, please do share it with us.
Keep it natural!