The term 'constitutional medicine' is one that causes confusion and consternation among homeopaths and patients alike. My understanding of the term is that, in some people, it is possible to identify a remedy whose picture matches the overall metabolism of the particular patient exactly. For that person, their reactions to stress, the way they behave when ill, the type of illnessess they get, all fit neatly into one remedy picture: children, and people who live in simpler, less technological and 'intellectual' cultures, may often present like this.
For these people, a dose of their constitutional remedy will raise their general level of health and when they are ill, the remedy will often cover their symptoms and bring healing. For many homeopathy users, the search for their 'constitutional remedy' is the Holy Grail, a recipe for permanent well-being, an answer to all their problems.
However, as life would have it, it is not always possible to identify a clear constitutional remedy for a patient. Maybe the remedy hasn't been 'discovered.' Or maybe the 'clear, pure tone' of the constitution cannot be heard clearly by the homeopath, due to the noise and complexity, the 'interference static,' of modern-day life. Drug use (pharmaceuticals and otherwise), on-going stress (a difficult relationship for example), and grief, can each contribute static to our lives (Hahnemann called this static "obstacles to cure"): giving a constitutional remedy without clearing the immediate, unresolved stressors, is like driving with the brakes on.
So when a remedy is determined, it may not be a constitutional one, the perfect, long-term deeper match; rather it might be a remedy to support the system in its stressed condition. Best I feel to offer a remedy to simply open communication with the patient's vital force, as expressed through the presenting symptoms, and worry less about finding the perfect match. The vital force, as I understand it, will do its best to communicate with the homeopath! Let the homeopath have ears to hear and eyes to see!