When someone is involuntarily admitted to a psychiatric hospital it is first for a 3-day evaluation period (this might actually be longer than 3 days if there is a weekend in there). Once this 3-day period is up, if the hospital finds the person a risk to themselves or someone else, they can re-commit the person for a longer period of time. This next period of time will vary but usually isn't more than 1-2 weeks. In rare cases, the hospital can petition a judge for longer commitments that can last a few months.
While there isn't much to do legally at this point, I would encourage you to express your concern to your wife's doctors on the psychiatric unit. They will likely want to know what kind of care she would be receiving at home if they were to release her, so you might want to have this set up prior to your talking to them (this would include outpatient psychiatric care, as well as having you or someone else available to her at home).