Belisarius: The Last Roman General by Ian Hughes is actually quite informative on this point. It summarises the changes in the Byzantine military (and in Byzantine society) following the fall of the West up to the time of Belisarius, a 6th century General under Justinian I.

Essentially, it isn't a case of the Byzantines throwing away the feats of technology they possessed and most of what they did 'lose' was military technology. Part of it was fate and part of it was practicality. There were both changes in style and forced changes of resources. The key strength of the Romans which had kept them militarily current for so long was that they had always taken any potential improvements they spotted in their enemies and used it to make themselves better at fighting them. We have a static image of Rome's army, but its core strength was that it was not static: it was dynamic.

A couple of major developments were happening around the time of the fall of the West. Back in the Crisis of the Third Century, it had become more important for the army to be able to move more quickly to defend against the multitude of threats. Thus there began a trend towards cavalry. A little later on, a specialised cavalry unit was implemented. Then the Huns arrived and whilst they were perhaps the last major enemy of Rome, they were also integrated into the Roman army. The Byzantines in particular used Hunnic techniques increasingly because Huns were a growing proportion of their technology specialists. This combined with Sassanid influences which developed in response to wars with the Sassanids in the East.

The fate elements are the battle of Adrianople and the fall of the West. Hughes explains that Adrianople, in which an Emperor and a huge number of Roman soldiers were killed, caused a massive loss of high-quality equipment. This combined with the fall of the West which led to most of the places which knew how to make that equipment being lost. The Byzantines were forced to replace those specialists with others from their other influences. I've linked some examples for the changes in equipment. The equipment lost at Adrianople and no longer able to be made after the loss of Italy is the sort in the first link. The main part of the helmet was made from a single piece of metal. However, this was a complicated and costly approach. The Hunnic and Sassanid influences the Byzantines were left with led to the increased use of ridge helmets. These had begun appearing from the end of the third century, but became much more common once the knowledge of how to make the single-piece helmets became much harder to come by.

http://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Helmet_typ_Weissenau_01.jpg/240px-Helmet_typ_Weissenau_01.jpg Earlier Roman helmet made from a single piece of metal. It was more similar to Gallic designs.

http://en.wikipedia.org/wiki/Late_Roman_ridge_helmet Late Roman ridge helmet made from more than one piece of metal joined with a ridge along the centre. This was cheaper and easier to manufacture. It was more similar to Sassanid designs, the influence on the Eastern border of the Byzantine empire.

In the West, the technology died away somewhat because to get that quality of manufacturing you need to have the resources and economy of a power like Rome. There's a big difference in scale between operating within the leading empire of the time and under a much more localised group. The West lost those with the authority, knowledge and resources to make things on Rome's level and instead had an influx of people who knew Germanic techniques.

What the Byzantines did preserve was classical learning. There were advances in Russia and the West after Constantinople was conquered by the Ottoman Turks in 1453, for example, because citizens from Constantinople fled there, and the Byzantines still received a proper Roman classical education.

If you clarify which specific "Roman technologies" you are referring to, I will answer as best as I can.