What is the ruling on a man who has abandoned his wife and children, except for infrequent visits and intercourse once every one to two weeks, for five years?

A husband is not permitted to abandon his wife in the manner described in the question. There are specific Shariah guidelines for abandoning a wife that must not be transgressed. It is obligatory for the husband to be just between his two wives. However, if a wife waives her right to equal division (of nights), she is permitted to do so. His children have a right upon him to maintenance, care, attention, upbringing, and guidance. Therefore, it is obligatory to advise this man to fear Allah concerning his family and children and to give every right-holder his due. Mere abandonment does not affect the continuation of the marital bond between the spouses.

And Allah knows best.