taper

To taper is to gradually grow smaller or more narrow or less intense. Taper is often used with the word "off." Part of the power of the Vietnam Memorial is in how the two walls appear to "taper off" into infinity.

It's a rare breed of person who can keep fighting for days and days and days. For most people, the desire for battle tapers off with time and exhaustion. The derivation of the word taper from the Latin papyrus is interesting but takes a while to explain. Your interest would taper off before I finished explaining it. The fact that a road appears to taper off into the distance is an optical illusion: It doesn't actually get narrower. It just appears to taper off.