If well maintained a sword can be usable for several generations. However, if you're talking about a knightly persona, while a sword may be passed down as an heirloom, the later in the period you go, the less likely it would be used in battle.
Sword technology and function changed enough over time to counter the changes in armor that it would be impractical to use a sword designed for the context of warfare several generations earlier. The single-handed type XII cutting sword and XIV cut and thrust of the early 14th century are rather limited in use in the hands of a late 14th century knight facing well armored opponents. No matter how much sentimental value their Grandfather's sword might hold, they're going to opt for a sword much more capable in the thrust with stiffer blade design like a type XVa, XVIa, or XVII.
In my living history group, our knight has his grandfather's sword in camp to show patrons, but makes it clear that it's more of an object of family pride than what he would use in a real fight. (This enables us to show earlier sword design while still being true to the history).
You also have to consider that by today's standards, knights and gentle men-at-arms (not counting the monastic orders, but even a lot of them were probably pretty rich despite their vows) were obscenely wealthy compared to the 3rd estate. As such they were very concerned with fashion and displays of wealth. So grandpa's sword may hold a place of honor in the house, but they're certainly going to have a modern blade as well.
TL;DR, it seriously depends on your persona and time period