There could be several different sorts of irrational action. Some actions might be irrational in the strong sense that the actor did not have much approaching a reason for the act. The person might "just be reacting". Another possibility would be actions for which the actor has reasons but for which s'he does not have anything approaching a good reason. In this case, one might act contrary to reason, and such an action might reasonably be called "irrational".

A really good answer to this question would need more context.

It's not irrational for me to fear that some harm will come to my children, even if I convince myself that if my children are in fact harmed, I won't find out about it. So Larkin was right.

It's irrational to fear what death will feel like if you know it won't feel like anything; but it doesn't follow that it is irrational to fear death. It's not irrational to look forward to the pleasures of living, and if we know that death will take these away, the fear of losing those pleasures doesn't seem irrational either.

The reasoning that in the absence of an afterlife it would be irrational to fear death dates back at least to the ancient Greek philosopher Epicurus, who wrote:

"Accustom yourself to the belief that death is nothing to us. For all good and evil lie in sensation, whereas death is the absence of sensation… Therefore, that most frightful of evils, death, is nothing to us, seeing that when we exist death is not present, and when death is present we do not exist."

There is a good collection of essays edited by John Martin Fischer called The Metaphysics of Death on this subject. Of particular interest to you might be the essay "Death" by Tom Nagel. Nagel argues (along similar lines to those used by Peter Lipton above) that there are things that can harm us (and thus that it would be rational to fear) that occur outside of our experience. Thus the mere fact that death is outside of our experience does not mean that it would be irrational to fear it.

Is this another way of asking whether belief in the existence of God must be irrational in light of God's intangibility? If so, I would answer No. There are many things that I cannot touch in whose existence I believe. For instance, I believe in the existence of Mars, but I'll never touch it. You might think that's a bad example because, while I can't actually touch Mars, I could in principle touch it: in theory, I could build a space ship that will bring me to Mars. God, on the other hand, seems to be something that I couldn't even in principle touch: according to many, God simply isn't located anywhere in the physical universe. But don't we believe in the existence of intangible things even in that stronger sense of "intangible"? For instance, most of us believe that the Equator exists, but it's not tangible (you can't trip over the Equator). Or, to take Richard's example, we all believe that the play A Comedy of Errors exists, even though it can't be touched, ripped up, or burned. Or finally, most of us think that numbers (like the number 8) exist though they don't seem to be at all located in the physical realm. So if one is irrational to believe in God's existence, that's not because God is something intangible.

Or perhaps you meant to be asking whether it's irrational to believe in an intangible God's existence on the basis of no evidence. If a person thinks the answer to that question is Yes, then God's intangibility again seems irrelevant: that person would likewise hold that it's irrational to believe in a tangible object's existence if one had no evidence at all for it. If there is irrationality here, its source is our lack of evidence and not the intangibility of the being that is believed to exist.