Capt. JG wrote:
....

The disadvantage is that each position depends upon the previous one, so
that small errors may build up to be large ones.

No, you can go a number of days referencing the last fix.

If you are on a long
voyage, you may find that the original stars are no longer visible at a time
when they are useful.

Yes, this is a problem.

Before this happens, you will need to pick some new
stars, and take a double round of sights - one for the fix, and one to
establish a basis with the new stars.

The other problem is that getting the compass bearing of a star is not
that easy.

I would recommend that anyone interested in emergency celestial
navigation get a copy of "Particularized Navigation: How to Prevent
Navigational Emergencies" by Francis Wright, which shows how to do "good
enough" navigation with paper sextants, etc. Unfortunately, its long
out of print, so a bit of work would be needed to adjust some of the
tables to current dates.

BTW, I own three sextants (two WWII vintage, one antique) plus two
"lifeboat" sextants, but I haven't taken a sight on board in a dozen years.