How was the Byzantine Empire able to survive so long, and what were its most important achievements?
The Byzantine Empire was a beneficiary of its geography. Constantinople's situation on the Golden Horn at the Straits of Bosporus meant that it was surrounded on three sides by water. The Straits themselves are very narrow, thus making them very easy to defend. On its land side, a tremendous wall protected the city. The wall was so wide that a team of horses pulling a chariot could be turned around on its surface. Those who attacked the city often found themselves subjected to a flammable and deadly concoction known as Greek Fire, which burned and was difficult to remove. It is entirely possible that the City of Constantinople would have survived longer had the soldiers of the Fourth Crusade not forced their way into the city by artifice and sacked it; from which it never recovered.
It's greatest achievement was the preservation of Roman Society and its learning. The Italian Renaissance benefited from scholars from Byzantium who travelled West after the collapse of the Empire. Constantinople was considered the "Second Rome" until its collapse in 1453. Additionally, Eastern Orthodox Christianity originated in Byzantium and from there was transmitted to large portions of Eastern Europe, including Russia. These areas still practice Eastern Orthodoxy as it was practiced in Byzantium.
The word "Ortho" means staright. It never deviated from its path. It recieved beating but never bent. Recieved pressure but never caved.
I am a Coptic Orthodox Christian living in the states. Most of the achievements that kept the Orthodox faith so fruitful and intact was the eccumenical councils that the Orthodox Church went through. The first being, the Council of Nicea that occurred in 325 AD which 318 bishops attended. The council put Arius on trial because he questioned the divinity of Christ. He stated that Christ was indeed God but less than God the Father. Pope Athanasius, from Alexandria defended the faith and established the creed still used today. The second council was of Constantinople in the year 381 which 150 attended; concerning "the Holy Spirit was a creation", stated Macedonius. Once again from the See of Alexandria, Pope Timothy defended the faith establishing that the HOly Spirit is equal in divinity with God the Father and God the Son. The third was the council of Ephesus in the year 431 which 200 bishopd attended. That council concerned the Constantinople bishop claimed that Christ was truly God but became God after the Epiphany. Stating that St.Mary was the Mother of Christ not the Mother of God. In Greek, Mother of God means "Theotokos". He called her "Christotokos". Pope Cyril of Alexandria defended the faith and excommunicated Nestorius. In the year 451 came the split of Roman Catholicism and Orthodoxy. The Coptic Church of Alexandria was known for its intellectuality so it usually was the center of the known world. Pope Leo of Rome set up a robbers council against the will of many bishops accusing St. Disocorus of Alexandria of blasphemy. Truly it was a political council because in the letter of Leo, he sent claiming Rome to be in charge. Pope Leo beat our precious Pope and ribbed his beard and plucked his teeth. That is the fruit of the faith. Without out precious fathers that suffered for the sake of preserving the right faith, the Orthodox belief would be extinct.