The poll of 542 Roman Catholics, published by the newspaper Reforma, reflected increasing concern about the hand tremors, difficulty in walking and slurred speech - all symptoms of Parkinson's disease - that make the pope's public appearances very taxing for him.
Thirty-one percent of those interviewed in the poll taken June 9 said he should come despite the health problems, and 11 percent did not answer. The poll had a margin of error of 3.8 percent.
A majority - 52 percent - said popes should retire from the papacy after a certain age or term of office, while 40 percent said they should remain in the papacy for their entire lives. The remainder had no opinion.
Those interviewed rated sexual abuse by priests a lesser problem for the Church than people leaving the faith.
While Mexico is generally estimated to be 90 percent Catholic, many of them are nominally Catholic and have little regular contact with the Church. Protestant churches have been making huge inroads among the poor and Indian groups.
Seventy percent said they had a great deal of confidence in the Pope, 52 percent in their local parish priest, and 38 percent in priests in general.
Most of the rest expressed ``some confidence'' in those churchmen, but 24 percent said they had little or no confidence in priests other than their parish priest.