I'm not sure what the problem is - but I can assure you that anacharis
does not die after growing to a certain length. I had it as the only
plant in a cichlid tank once and would routinely pull 2 to 3 foot long
shoots of anacharis out of the tank and throw them away.

However if you are growing it rooted and the top covers the surface the
problem may be as simple as the top of the plant cutting off light to
the bottom of the plant and causing it to die. I always grew mine
floating on top of the water. But that's just a guess - I really have
no idea what the problem is, just letting you know what the problem is
not ;-)

-Daniel