Ethiopia's long survival allowed it to develop a national identity which was in no small part due to the unifying force of Christianity. Finally (as commented on by jamesfq), its terrain, although making it difficult for some emperors to enforce unity in more than just name, also made it difficult for foreign invaders to conquer.
As a side note, it is worth pointing out that, while the influence of the US was important for Liberia, it was not the only factor which helped that country maintain its independence (and Liberia did lose some territory).

Unity, Identity and Development
Christianity in Ethiopia dates back to the 4th century. Although never an active participant in the European crusades, the unity of Christian Ethiopia was instrumental in limiting Muslim incursions:

By the end of thefifteenth century, the Christian kingdom had for all
  practical purposes imposed its will over its enemies.

Source: Saheed A. Adejumobi, 'The History of Etiopia'
Although Ethiopia subsequently fell into disunity, the accession of Emperor Tewodros II (ruled 1855-68) led to the re-establishment of a strong, unified state before the scramble for Africa began in earnest. Further, Tewodros wasted no time in pursuing his goals of unification, reform and innovation:

After his coronation he marched into Wallo, and seized the natural
  mountain fortress of Magdala which was to become his capital. Later in
  the year he overran Shoa, the last Christian province outside his
  control...

Source: R. Pankhurst, 'Ethiopia and Somalia', Chapter 15 in A. Adu Boahen (ed), 'A General History of Africa, volume 6 (UNESCO)
Tedowas also built roads