Answer:
False
Step-by-step explanation:
No. Comets that come close to the sun lose mass every time they do so (as they are heated up, they lose gas and dust). Eventually they run out.
Comets that stay out in the Oort cloud, away from the sun, last basically indefinitely.
For instance, old earth creationist Hugh Ross claims that the lifespan of Halley's Comet is approximately 10,000 years, whereas others comets have given an average lifespan of approximately 2,000 years (Ross 2004: 202). ... Orbits of comets are divided into two categories, long period and short period.
Some of them, yes. Comets that remain orbiting the Sun in the Kuiper Belt or the Oort Cloud have extremely long, indefinite lifespans.
The comets that *we* actually observe with the naked eye, that being those that are are nudged or knocked into an orbit that takes them into the inner Solar System, have very short lifespans, in the range of thousands or tens of thousands of years.