At first, the absence of direct military intervention from the great european powers. The first Balkan War was concluded rapidly as the Ottoman army was busy fighting the Italians for Libya. The Second Balkan War, that started merely a month after the end of the first, opposed the former winners against Bulgaria. Again, the forces where not equal and the influence of the great Powers stayed relatively diplomatic instead of military. Astonished by the victories of the slavic forces, Austria-Hungary only intervened after the end of the second Balkan War. More so after the assassination of Franz - Ferdinand. The declaration of war between Austria-Hungary and Serbia then played the web of alliances between the east european and european nations, bringing them all in a war with much more players and military potential.

TLDR: in the Balkan Wars, Europe looked from afar, playing their diplomatic strings. The situation escalated until much more players were involved, thus spreading the First World War on 4 years.

For more information on the history of the Balkan peninsula, Bogdan, Henry.From Warsaw to Sofia: A History of Eastern Europe, 1989.

In the case of the first war, the Ottoman Empire was suffering from a great deal of internal strife as well as military reforms that were ongoing when the league decided to attack. Just four years earlier the Young Turk revolution happened.

Additionally according to Richard C Hall in his book "The Balkan Wars", it was logistically very difficult to transport everything needed to defend a vast area, as it was stated that the entire area along where the attack happened would be defended.

In "A Military History of the Ottomans: From Osman to Atatürk", by Edward J. Erickson, he states that:

In the fall of 1912, the Ottoman political and military leadership was caught completely by surprise and was unprepared for the aggression of the Balkan states. The army’s seasoned recruits had just demobilized (more than 70,000 soldiers) and, moreover, many talented officers were fighting against the Italians or were on their way to join the war.

A reinforced divisional group under the command of Chief of the General Staff Ahmed Izzet Pasha (composed of 29 crack battalions from First, Second, and Third Armies) had just suppressed a rebellion in Yemen and were too far away to return to the war zone on time. The infant army corps and triangular divisions, which were still battling to finish the reorganization, did not have the means to overcome the efflux of trained and seasoned soldiers and the influx of untrained raw recruits.

Furthermore, there was a serious political crisis in which different partisan officer cliques were doing everything possible to establish political control and exterminate their rivals.

Coupled with this, Ottoman political and military leadership obstinately determined to preserve every inch of the empire’s territory, and they had great faith in the military capacity of territorial defense units.

I'm not too sure about the second war, but it appears something similar happened there, a grossly outnumbered army of one nation (Bulgaria) simply couldn't defend against a numerically superior military from a wide front.