Well, let's put Alexios into context. He wasn't necessarily breaking an ancient line of inept rulers--rather, in the years prior to his coming to power, the Empire was disrupted by the arrival of the Seljuk Turks in Anatolia. Under Romanos IV the Byzantines were defeated by Alp Arslan at the Battle of Manzikert, and Romanos IV was captured in battle and held captive. Following his capture there was a great deal of political discord in the Empire--the next two Emperors, and Alexios Komnenos himself, came to power via violent uprisings.

So Alexios is not so much an example of good leadership breaking centuries of uniquely awful leadership, but he might be more accurately characterized as a good leader who brought an end to a period of civil strife and allowed the Byzantines to focus once more on their outside enemies such as the Turks and the Normans.

Putting Alexios Komnenos aside, can we make a case that the Byzantines had unusually ineffective leaders? I think that is challenging to prove--they certainly had their share of inept leaders and were in a state of frequent decline, I don't know that you can firmly conclude that Byzantine rulers were less capable than their Western European or Middle-eastern counterparts. It is true that Byzantine leadership even prior to Manzikert had generally seen more failures than successes, and most of the leaders in the roughly 50 years between Basil II and Alexios Komnenos were not effective. But that period doesn't necessarily indicate a general trend of inept leadership for the Empire's total lifespan. The Empire actually enjoyed fairly effective leadership throughout the late 9th to early 11th century under the Macedonian dynasty. It was only during the mid-11th century that things really started to collapse, especially after the arrival of the Seljuk Turks in Anatolia.

I think there are two factors which contribute to the Byzantine reputation for poor leadership:

• first, the fact that when their leaders screwed up, the consequences were dire. The Byzantines were sort of stuck between a rock and a hard place--the Turks and Arabs threatened them to the east, the Bulgarians and Turkic steppe peoples threatened them to the north, and the Italians, Franks and Normans to the west were fair weather friends at best and deadly enemies at worst. It is much easier to argue that, rather than being victims of bad leadership, the Byzantines were victims of far greater threats to their power than other groups in Europe, and therefore any missteps by their leaders were greatly amplified.

• second, the lack of well-defined succession laws. This gives the Byzantines the (somewhat unfair) reputation as a bunch fratricidal usurpers, and many of the worst missteps of the Byzantine Empire are the results of contested succession results (e.g. the aftermath of Manzikert, the reign of Andronikos Komnenos, and the 4th Crusade). But again, can we really argue that the Byzantines were unique in their succession difficulties? Even in the west where there was a more clear tradition of leadership passing from father to son, the death of leaders frequently led to contested succession... not to mention the fact that the fluid succession traditions of the Byzantines actually led to some competent leaders (the Macedonian dynasty was founded with the murder of an Emperor; Alexios Komnenos came to power via usurpation).

So in conclusion, I challenge the idea that the Byzantines were cursed with a long-standing trend unusually bad leaders. The Komnenid dynasty broke a pattern of decline, yes, but that decline was really only over the course of 50-60 years, preceded by the mostly effective leadership of the Macedonian dynasty. I think that, rather than looking at the Byzantines during these years and saying "wow what a bunch of screwups", it is more reasonable to conclude that they faced a huge number of challenges in the 11th century such as the arrival of the Turks in Anatolia and the Normans in southern Italy. These challenges amplified the mistakes of their leaders greatly, but the decline of the empire during this time should not be attributed to a general trend of poor Byzantine leadership or any specific structural issue which led to unqualified leaders. The Byzantines were surrounded by enemies for most of the middle ages, and their decline and ultimate destruction is more fairly attributed to an overabundance of hostile neighbors than any internal failure.