My brother lost his wife one year ago and he's still incapable to resume his social activities and interest: is this normal? Is there something we can do to help him?
The outcome of normal grief is, by definition, resolution.
How long this takes is difficult to state since there is no clear end to grief. Older psychiatrists tended to think in terms of months or a year, but it's now recognized that the bereaved may have symptoms from time to time for much longer.
Most experts think that getting over bereavement cannot be compared to the way one recovers from an illness or an accident, but rather to adjust to what happened, achieving a new life-style which may be different from the one before bereavement, but is also satisfactory.
Bereavement counseling, like medication, can be effective when is given to those who need it; but this it's not always easy to determine. Providing counseling to a person who is likely to cope well without it may be more harmful than good, by undermining his confidence in his own resources and encouraging unnecessary regression and dependency.
On the other hand, counseling the more vulnerable is known to reduce morbidity and enable some of those who would be expected to suffer from abnormal grief to do as well as similar individuals who were not so handicapped.
To make a long story short, my suggestion is to ask for an expert opinion by suggesting your brother to go and see a psychiatrist or a psychotherapist to assess his present state.