It's a fairly well established fact that the early middle ages were a period of intense deurbanization in most of Europe; the first major population recoveries did not begin until the 11th century, though they quickly built up steam. So: my question is, during a period in which cities basically do not exist, and the largest settlements in a given kingdom are a handful of towns of 1,000-10,000 individuals, and the vast majority of the population lives hand to mouth in agricultural settlements, how did skilled craftsmen function?
A sword, for instance, is a very specialized tool, requiring advanced knowledge far beyond that which a common blacksmith would possess. Would these bladesmiths cluster in the few towns, and anyone who wished to purchase one would have to make the trip in from the countryside?
Military equipment crafting is definitely something that didn't die out because of the necessity, even in places like Britain where civilian production of what was previously common items like wheeled pottery disappeared. The increasing militarization of society in all levels in Europe and the needs of the social economy dictated the survival of particular crafted goods. The need for elites to provide for the defense of themselves and their warbands/retinues never declined though the need for say, monumental building construction did.
A rough contemporary analogy can be made with Afghanistan in the aftermath of its civil wars but before the US invasion, in that there were still workshops producing and repairing AK-47s (on a rather crude but functional basis) even though they weren't manufacturing much else as a primarily agrarian economy.
However for other artisanal manufacturing, the question is still up in the air. For example, the restart of church construction in Italy in the 8th century points to a surviving artisan community which could furnish those churches with mosaics, light fixtures, decorative work, as well the knowledge of how to build new churches in stone (most new buildings were built out of wood at this time in Italy). However the more than 100 year gap between new church construction raises the question of how exactly those artisans survived that dormancy. One possibility being they may have been imported from the eastern empire, or they may have come from merovingian france, but those are just possibilities. No one is quite sure who those artisans were or where they were from, whether they were in fact local or foreign.
tl;dr - Don't assume technological decline was uniform in all things. The skills that were needed by the society of that day flourished. Those that weren't, withered.
Sources:
Christie, Neil. The Lombards: The Ancient Longobards. Oxford, UK: Blackwell, 1995.
Ward-Perkins, Bryan. The Fall of Rome: And the End of Civilization. Oxford: Oxford UP, 2005.