Why would they cease to exist? They'd die from being so perfect?

You also asked what would be the purpose from then on. The "purpose" is probably to recreate life, and enjoy the one you have. What is the purpose of having a purpose?
What I mean is if we were to become perfect it would be in one of two ways perfection within ourself or emotional perfection and/or primal instinct perfection to reproduce children with an immunity and adaptability to cope with the disease and pollution etc that is changing our world, do those two things and one would be perfect.

Aren't we so hard bent on trying to have the perfect life that we have lost sight of what our real existence is for .like you said it is our primal instinct to reproduce and carry on the human races existence and hey maybe in years to come someone will give birth to a perfect baby a baby who can never get sick, is immune to all disease and has an advanced learning capability, I don't think its the fact that some ne perfect excels in maths or science as I think someone said earlier but has a huge capacity to learn and adapt to the ever changing world.

On another note I said what would be the point in continuing well yes to reproduce of course but if we ever did reach perfection would we ever realise it or just lose sight of what perfection is or as you said I think do we really know what the limits of perfection are so maybe therefore we would never know if one self became perfect.