Yes, the princess mentioned in the Jean Sasson book "Princess", named Princess Sultana is still alive.
Most recently the author shared with readers on a blog that she recently met with Princess Sultana in 2013 to discuss a new book that will be another true story about the princess, due out in 2014.
(Note: if you're referring to the older Saudi Princess, named Sultana bint Abdulaziz Al Saud, she was born in 1928 and passed away in 2008.)
Sultana bint Abdul-Aziz Al Saud died in 2008.
Saud Nasser Al-Saud Al-Sabah was born in 1944.
Saud Nasser Al-Saud Al-Sabah died in 2012.
Sultan Al-Saud was born in 1985.
Saud Al-Shuraim was born on 1964-01-19.
Saud A.S. Al-Rasheed was born in 1981.
Khalid Saud Abd Al Rahman Al Bawardi was born in 1977.
Saud Hamoud 'Abid al-Qatini al-'Otaibi was born in 1971.
Al-Bandari bint Abdul-Aziz Al Saud died in 2008.
Al-Bandari bint Abdul-Aziz Al Saud was born in 1928.
Saud bin Saqr al Qasimi was born in 1956.
Saud bin Muhammed Al Thani was born in 1964.