if the Democrat does not control a Farmer space in the country of the next Power Struggle, does he retain the card in front of him until a Power Struggle occurs in a country that he does control such a space in?
No, he doesn't. From the clarification and correction page (www.wargameroom.com/1989faq.htm):
72. Peasant Parties Revolt: The Farmer space must be in the country of the Power Struggle. Removed after the next Power Struggle whether the Democrat controls a Farmer space or not.