This may help:
"There is no hard-and-fast rule over what happens to suffixes when the
most senior of the name dies. Do the men retain their titles, or do
they all "move up" one? Neither tradition nor etiquette provides a
definitive answer (columnist Judith Martin, for example, believes they
should all move up, but most agree that this is up to the individual
families). Upon the death of John Smith, Sr., his son, John Smith, Jr.
may decide to style himself John Smith, Sr., (causing confusion if his
widowed mother and his wife both use the formal style Mrs. John Smith,
Sr., and necessitating that his son and grandson change their titles
as well) or he may remain John Smith, Jr. for the rest of his
lifetime. One advantage of moving up one is that it eliminates the
extension of Roman numerals over the generations: i.e., a John Smith
III, IV, and V. A disadvantage is that it may cause confusion with
respect to birth certificates, credit cards, and the like."