I don't know if there is a specific life of a water pump, but the water pump on my car (see my signature, same engine as yours) went out earlier this year, and in fact, I had forgotten, but that is exactly how it went out.
I was loosing coolant, couldn't find a leak, but I finally noticed it leaking when I let it idle in my driveway. It was the water pump leaking.
2001 E430, Bourdeaux Red, Oyster interior.
1973 280SE 4.5, 170,000 miles. 568 Signal Red, Black MB Tex. "The Red Baron".