The length of time you can book a rental for is subject to the inventory of the supplier. When renting a vehicle from Tan Son Nhut Intl it should be possible to rent a car for a whole month if needed.
View Dollar locations at Tan Son Nhut Intl
64 Road 38
Ho Chi Minh City 700000
View Avis locations at Tan Son Nhut Intl
44 Vu Tong Phan Street
Ho CHi Minh City Airport