Well, here's my guess....

The only thing I can think of that would make it break is that it's
being hit by a connecting rod and it breaks at the weakest spot ,which
is where that fill line is scribed on it.  As to why it's being
hit...hmm. My memory may be wrong but I think I've seen some engines
where there is a dipstick tube that extends down into the engine to
make sure the dipstick is kept away from the moving parts.  Perhaps
there are two separate dipstick tubes, one on the outside, the one you
have replaced, and one on the inside, which has perhaps simply fallen
out and is laying in the oil pan.  So now when you stick the dipstick
in it's just flopping around inside the engine and getting hit.

Or if there is just one tube that extends from outside the engine to
inside is it curved in anyway on the lower part so that you have a
choice of how it's "aimed" on the inside?

Before the tip breaks off have you noticed any marks on the end of the
dipstick indicating something is hitting it?

--
Elbridge Gerry, of Massachusetts:

"What, sir, is the use of militia?  It is to prevent the
establishment of a standing army, the bane of liberty.  . .
Whenever Government means to invade the rights and liberties of
the people, they always attempt to destroy the militia, in order
to raise a standing army upon its ruins."  -- Debate, U.S.  House
of Representatives, August 17, 1789