Simply speaking a submissive is rebelling when he/she completely ignores the dominant's rules or does the exact opposite of what they are supposed to do. For example: A submissive has rules about what they can wear, language they use and certain tasks they must complete daily. Were this submissive to rebel, he/she would wear clothes the dominant would not approve of, use words the dominant forbade, and not complete any of the tasks set for them. In this way rebellion is a complete withdrawal of any submission and a blatant disregard for the rules of the relationship. 

When a sub acts this way, the first response of many dominants is to quell the rebellion. Often punishments are used as an attempt to correct the behavior and discourage the submissive from repeating the behavior. When punishment fails to work, releasing the submissive is usually the next choice. Unfortunately, this approach leaves a lot of hard feelings on both sides and completely ignores the fact that rebellion is often a major sign that something is seriously wrong with the submissive or the relationship. 

Most submissives do not rebel for no reason. If it occurs, it is usually caused by some kind of mental or emotional conflict within the submissive. This upheaval could be caused by any number of things such as work problems, an argument with the dominant, or other outside stresses that have gone unresolved for some period of time. Because most submissives do not rebel for no reason, it becomes imperative that the dominant try to find out why this is happening, before punishing for it.  

In many, if not most, cases the rebellion can be resolved by discussing what is going on with the submissive. This does not mean to ignore or condone the behavior. It does mean that finding out what is behind the behavior and resolving those things, will have a better chance of stopping the rebellion than just punishing for it would. Punishing a sub who is rebelling due to inner conflict will serve only to increase those inner conflicts by adding such emotions as anger, resentment and fear to what is already there. This will often make the behavior worse rather than better. Because of this, locating the problem, discussing it and changing things if needed to resolve the issue, is the better course of action. 

Once the underlying cause of the rebellion has been resolved, the submissive will most likely return to their usual behavior patterns. At this time punishment for the behavior can be done. However, it is extremely important that the submissive know and believe that the punishment is for the behavior, not the underlying cause of it.  

Rebellion can often occur in a relationship where the submissive partner is new to BDSM. The underlying causes are then usually fear of their feelings, confusion about what they were taught and being submissive, and/or not being used to discussing emotions before they reach a critical point. These things will usually resolve themselves over time as the submissive becomes accustomed to their chosen role and the level of communication involved in a d/s relationship. 

In some cases, the reason behind the rebellion can not be resolved. Or they are of such a nature that the relationship itself is badly damaged. If this is the case, then releasing the submissive would be the best course of action. 

Rebellion is not easy to deal with, but it can be worked through if both people involved strive to do so.