UPDATE 5-Storm Nate weakens, oil contractors found in Mexico

* Storm Nate fizzles after landfall on Mexican coast

* Oil-exporting port Cayo Arcas remains shut

* Six contractors survived, three dead, one missing (Updates with rescued contractor dying, weather)

By Roberto Ramirez

GUTIERREZ ZAMORA, Mexico, Sept 11 (Reuters) - Storm Nate dissipated on Sunday as it moved farther inland across the coffee and sugar growing state of Veracruz along the Gulf of Mexico.

Nate, which could still dump heavy rain over Veracruz, had turned into a remnant low, the Miami-based U.S. National Hurricane Center said, and it was discontinuing warnings.

State oil monopoly Pemex said it had rescued seven out of 10 contract workers who had been missing since Thursday after evacuating a rig in the Gulf of Mexico due to bad weather.

The workers, including four Mexicans and two Americans, were rescued in the Bay of Campeche, but one Bangladeshi died later in a hospital. Two other workers were found dead and one remained missing, Pemex said.

The depression was located 75 miles (120 km) west southwest of Tuxpan, with maximum sustained winds of 30 miles per hour (55 kph), the hurricane center said in its 10:00 p.m. CDT/0500 GMT advisory. It is moving west northwest at 8 mph (13 kph), it said.