Why don't the people of Ember know the actual date in Jeanne DuPrau's The City of Ember?

In Chapter 2 of Jeanne DuPrau's The City of Ember, Lina is charged to deliver a message to the mayor in person. While waiting in the reception room to the mayor's offices in the Gathering Hall, Lina reads through a book titled The Book of the City of Ember that describes all of the amenities and functions of the city. While reading about the important function of the timekeeper and the Gathering Hall clock, she recalls that "not all timekeepers were as faithful as they should be," which is why no one in Ember can really be certain of the exact date and time.

Since Ember is underground, it is surrounded in complete darkness. The citizens rely on lights being turned on and off to be able to tell when it is daytime and when nighttime. Since they have no other means of telling time without the sun, moon, and stars, the citizens of Ember rely only on the city's clock, the date sign,  and the timekeeper. Lina recalls hearing that there was one timekeeper, "some years ago, who often forgot to change the date sign, so that it might say 'Wednesday, Week 38, Year 227' for several days in a row" (Ch. 2). There were also timekeepers who completely "forgot to wind the clock," which would make the hands of the clock stand stationary for hours at a time, creating very long days and very long nights. Lina reflects the consequences of poor timekeeping in the following:

The result was that no one really knew anymore exactly what day of the week it was, or exactly how many years it had been since the building of the city. (Ch. 2)

Poor timekeeping ties in with the major premise of the book, since the Builders could only give the city enough provisions to last about 200 to 220 years. Therefore, if the actual year is closer to 250, then the city is very close to disintegration, and the citizens must find their way out.