Dear Dario,
You are right, there is indeed a problem with precession for
very distant dates. It gets even worse if you go further into the
future or past.
The "standard" IAU formula for precession gives the motion as a
cubic polynomial. That polynomial gives essentially zero precession
at the present, and for dates 25000 years ago and in the future
(when the earth's axis is again near Polaris), with maximum
precession in between. It gives a very close fit to the actual
precession for dates near the current epoch, but as you noted,
it diverges outside that range.
I believe there are formulae for precession for really distant
dates/times, going into the millions of years realm, sacrificing
current-day precision in exchange for covering a longer time span.
But there are few aspects of Guide that are really accurate for
such distant dates anyway. For example, the planetary positions
start to diverge from reality when you get more than about six
millennia from the present (the range over which the VSOP terms
were computed). The earth's obliquity starts to vary wildly,
indicating that our caveman ancestors lived in an era where the
earth's axis was in the plane of the ecliptic, and there were
six-month days and six-month nights all over the earth:
http://www.projectpluto.com/accuracy.htm#distant
As is pointed out at the above, if you go further into the
future, you learn that the earth will crash into the sun sometime
around 74000 AD.
In fact, about the only things in Guide that can be trusted
dozens of millennia from the present are the star positions.
(And even they have some fuzziness; click for 'more info' on
a star, and you'll see that the uncertainty in the position
can be quite high.)
-- Bill