How do you know God isn't dead?

[lordxenu]

why is assumed that he is still alive and well?

This largely depends on which religion you pose the question to.

In many religions God is not exactly alive so as to die. Moreover, in those same religions, God is immortal he or she cannot be destroyed.

In other religions Gods do die. In Christianity, Jesus dies on a cross, only to resurrect again (hits vid_restart on the rcon panel).
In ancient Egypt, it was believed that Osiris died and was resurrected by Isis using a spell she learned from her father.

It is true that the power of Gods seems to diminish as science and logic prevail but that is something different. It has to do with us (humans) using God as an answer to that which was mysterious and unknown.

In practice, God dies when people stop believing in his existence. So Zeus, is dead, but Rama is not.
I doesn't matter if the God really exists in the first place. What matters is that there are people who believe in his existence and are acting accordingly.