So basically 不停 and 不断 mean the same. But 不断 is like without any pause,e.g. 音乐声不断。(It could mean that someone is playing music over and over again)音乐声不停。(It could the music never stop even without changing it.) In oral English,don't bother with these two,both are fine. 不息 is more literary*,being used in literature or paper work.

你好，我会提出我的建议，但可能不全正确。 There's a old sying:an apple a day keeps the doctor away,but on one says"a banana a day keeps the doctor away"."不绝于耳"，"生生不息"也一样，他们就如同小型的谚语一样。中国人把一些四个字的古代的词语叫"成语"（但不是所有四个字的词组都是成语），这些成语是不可以随便改变的。并且，中国古代的文字和现代的文字很不同，中国的孩子的中文课除了学习现代文章之外，还会学习古代文章和诗歌。我是个初中学生，事实上，如果没有解释，我不能很好地理解古代的文章和诗歌的意思。比如"环滁皆山也"意思是，滁州郡周围环绕着山。古代文章和诗歌更简洁，也更难理解。

Following on from Cara's advice and explanation, it seems to me ultimately counter-productive to compare a few words without context, in a vacuum. The intelligent learner would always state, and work from, the context in which they first encountered a new word. That context is the fertile soil in which understanding may blossom. Usage, 用法，is not mastered through an abstract discussion of definitions. Life, and communication, is at the end of the day, not a dictionary. One should of course look up a dictionary on one's own first. That is the very minimum work that one should put in first before coming here. Italki is first and foremost a mentoring community. It is not a dictionary. Students, having looked up a dictionary, come here to say exactly which parts of the definitions they have a problem with. Cara 生生不息的例子很好。Collocation 嘛。 "好歌唱不停"， 就没有人说"好歌唱不断"。 "连绵不断"， 就没有人说"连绵不停"。 "不绝于耳"， 就没有人说"不停于耳"。 一般人是怎样学会的? 按课本循序渐进，多看书，多听普通话广播，就会了。中国小孩从来不是通过发问"请问不断、不停和不息有什么不同"之类的问题来学会中文的。那是死胡同来的。 用好的方法来学习是关键，方法不对，就会事倍而功半。

a brilliant question 不断 means continue ,unceasing,uninterrupted,constant… for example. continual readjustment.uninterrupted growth.march on without cease. 不停 means without stop.it can be used in many places. 不息 this word is a little abstract…it is usually use with life,nature and it's very formal . it also means no stop. hope this can help you :) for example: life and growth in nature.the circle of life.endless struggle.

不断 unceasingly 不停 continuous, no pause 不息 untiring