When an addict begins the path of sobriety, he must be willing to be separated from the object of his obsession for the rest of his life. He may only be able to endure the thought of being separated for a a short time, even an hour ("I'll have a drink later, just not right now"). But, this is still with the understanding that real sobriety is a desire for permanent abstinence.
The addict who harbors ambitions of returning to abusing will eventually do so.
In the Church, there are is an often misunderstood concept of 'fasting.' Sometimes, we think of abstinence in addiction as a type of fast, which is true in some ways but not true in others.
Fasting in the Church centers around the notion that what we fast from is not necessarily bad, but rather we need the spiritual exercise of denying ourselves certain things to weaken our self-will and bring out the hidden passions that must be cured. In some respects, an addict could relate to such a fast: alcohol is not necessarily bad, but its abuse leads to the avoidance of our fears, which in turn feed the passions.
But, in addition to fasting, the Church teaches 'feasting.' We return to the things which we fasted from, not to over-indulge, but again enjoy properly. Addictive abstinence has no return. The alcoholic never goes back to drinking. He can never plan to control and enjoy his drinking at some later date, because the disease has affected him in such a way that the control mechanisms that others have he no longer has.
Fasting is about exercising control, with God's help, but the addict's abstinence is about a permanent loss of control. Even the monk who fasts from meat year-round can have a dispensation to eat because of health issues or circumstances. The addict cannot return, except (depending on the addictive object) when under supervision and even then it must quickly end lest a relapse occur. Food addicts have a truly difficult path: no one can go without food, and so they must have a very regimented dietary approach.
What both fasting and addiction-abstinence teach is how to confront the passions without avoidance. We must stop avoiding our passions and repent of them. We must dig deep to repent of our fears and receive God's healing. Fasting gives us this opportunity on a temporary basis, which is why there is always an end to the fast, marked by a feast. We return with joy. The addict never returns to his addictive substance with joy. Yet, the self-denial of both acts reveal the passions.
Christians are expected to permanently abstain from sinful behavior, such as idolatry and fornication, and yet identify themselves as sinners who do such things. It is very close to if not the same as the notion of being a sober addict: just because the addict is not acting out on his obsession does not mean he isn't an addict anymore. Christians who abstain from sin are not to think of themselves as no longer sinners. In both cases, thinking you are 'cured' leads to a lackadaisical attitude which ends up in relapse.
Addicts can benefit from fasting, since it exercises the will in areas that the addict still retains control. Some addicts fall into the trap that since they abstain from their addiction they have enough spiritual exercise and so they indulge in their unrestrained self-will in other areas. This is not helpful.
Neither should Christians who are not addicts assume that they can resist their own temptations enough to immerse themselves in what is tempting without risk of engaging in the behavior. An addict knows he cannot go into places of temptation without risking a relapse, yet many non-addict Christians routinely engage in risky behaviors that put them in danger of falling into sin, then wonder why they fall.
I wish there was better terminology in English to describe the different between fasting and permanent abstinence, but we are stuck with the language that we have. My hope is that addicted and non-addicted Christians will understand that fasting (as a periodic and temporary discipline) is beneficial for spiritual development, and that objects of obsessive temptation are not fasted from, but permanently avoided.