Purists probably won't like this but ...
When you get to the point of applying kote-gaeshi (twisting the wrist) and it doesn't work:
1 You need to re-examine how you got to that point and what you missed out or did wrong - timing / taking balance etc. - the typical answer, and the necessary one to improve your Aiki technique.
2 You also, in my opinion, need to be able to use your body against their wrist in such a way that you can FORCE uke down regardless. Uke has one way out - to fall down away from the PAIN. Otherwise, their wrist will BREAK. It breaks not because you forced it, but because they refused to fall. Once you improve your forcefull method, you will have more confidence at REAL self-defence - the main reason many beginners step into the dojo in the first place (before being bamboozeled by peace and harmony). With this method, it is important to clearly negotiate the training regimen with your partner / class. It is not a nice way to train, and interestingly, after one or two goes at it, ukes fall without resisting too much as, well, it is just too painful to keep resisting!
3 Follows on from '2' in that, if one tech fails (kote-gaeshi), it can be modified by say, quickly applying waki-gatami to break balance and then returning to kote-gaeshi (if it is kote-gaeshi that youreally want to do). In this way, you don't need to stop and start all over again everytime your tech hits a glitch. ... As they say, "How you train is how you fight."
#1 is the best way to improve your tech, and #2 & #3 are also legitimate (necessary even) ways to train, in my opinion.
Note: If you are a beginner, you should not use any force at all, and neither should uke overly resist. In the beginning, you should just learn the shapes and general movement.