Fundamentally, we don't know. Only a small fraction of the Medieval swords ever made have survived (sure, there are many surviving Medieval swords, but there were many, many times more swords out there in the past), and the survivors are often special - e.g., preserved due to being owned by a VIP. If older swords stayed in use because they were cheap (which seems to have been the Late Medieval case), looking at swords owned by the wealthy tells us little about the cheap end of the sword market.

Perhaps worse, many swords were found with no context to provide a reliable dating - our estimates of the ages of such swords are based on the styles of the blade and hilt, which tells us approximately when the sword was made, but not how late it saw use.

In some cases, old blades have been found which had been fitted with much later hilts - in some cases, the hilts are hundreds of years newer than the blade. Thus, we know that some old blades remained in use. We also know that old swords were often sold cheaply in the later Medieval period (e.g., from values given for old swords in wills, and other textual sources). But we don't know how common such old blades were.

In the early Medieval period, we know from literary sources that old swords were valued. This was a time when swords were still quite expensive, and would be passed down as valuable heirlooms. Also, at a time when metallurgy was only poorly known, and the heat treatment of steel to produce blades with hard but tough edges was a crap-shoot, old swords which had survived repeated use in battle had proven their quality.

Some examples old swords:

The famous sword Tizona, supposedly wielded by El Cid, with a blade in 12th century style, and a 15th century hilt:

• https://commons.wikimedia.org/wiki/File:Espada_Tizona.jpg

Another sword attributed to El Cid, called Colada, has a possibly 11th century blade, together with a 16th century hilt.

The Vallstenarum sword (found in Gotland in the Baltic) has a blade that appears to date to about AD500, and the hilt was modified or replaced c. 600.

The sword Sköfnungr appears in a Viking saga set in the 6th century, and also appears in sagas set in later times: it appears in the early 10th century, and again in the early 11th century, and was still carried in the late 11th century. Perhaps the 6th century appearance is purely fictional, but in the later less-legendary sagas, Sköfnungr was in use for about 200 years.

Finally, a basket-hilt sword (from the 17th century?) was found to have a pattern-welded blade typical of the early Viking Age.