Don't think so, just because something has a end state does not mean it will ever reach it.
Don't think this is a good analogy but...
to say that death is the end of life suggests that all living thing die.
I agree with you, just because death can occur to life, it does not mean that it will occur to life.
Take this (not very good) analogy for example
Let's say that life is like a dry woollen cloth, and death/the end of life is a soaked cloth.
If we submerge a dry woollen cloth in water it will get soaked, this is analogous to a living thing dying.
As long as someone does not submerge the woollen cloth in water it will not get soaked. Analogous to the life continuing. If the cloth never becomes submerged in water it will never get wet
That is all assuming that having a woollen cloth will soak it is a absolute fact
So just as a woollen cloth can be submerged in water and can get soaked, thus does not mean that it will be submerged in water, death being the end of life does not mean that all living things will die
But others have already noted, that is not implied in the statement, it merely states that life having an end **suggests ** that life will eventually end.
In a sense it does but I think this is more due to the power of suggestion or something to do with our psychology.