By now I expect most of us have acknowledged the importance of being rational. But as vital as it is to know what principles generally work, it can be even more important to know the exceptions.
As a process of constant self-evaluation and -modification, rationality is capable of adopting new techniques and methodologies even if we don't know how they work. An 'irrational' action can be rational if we recognize that it functions. So in an ultimate sense, there are no exceptions to rationality's usefulness.
In a more proximate sense, though, does it have limits? Are there ever times when it's better *not* to explicitly understand your reasons for acting, when it's better *not* to actively correlate and integrate all your knowledge?
I can think one such case: It's often better not to look down.
People who don't spend a lot of time living precariously at the edge of long drops don't develop methods of coping. When they're unexpectedly forced to such heights, they often look down. Looking down, subcortical instincts are activated that cause them to freeze and panic, overriding their conscious intentions. This tends to prevent them from accomplishing whatever goals brought them to that location, and in situations where balance is required for safety, the panic instinct can even cause them to fall.
If you don't look down, you may know intellectually that you're above a great height, but at some level your emotions and instincts aren't as triggered. You don't *appreciate* the height on a subconscious level, and so while you may know you're in danger and be appropriately nervous, your conscious intentions aren't overridden. You don't freeze. You can keep your conscious understanding compartmentalized, not bringing to mind information which you possess but don't wish to be aware of.
The general principle seems to be that it is useful to avoid fully integrated awareness of relevant data if acknowledging that data dissolves your ability to regulate your emotions and instincts. If they run amok, your reason will be unseated. Careful application of doublethink, and avoiding confronting emotionally-charged facts that aren't absolutely necessary to respond appropriately to the situation, is probably the best course of action.
If you expect that you're going to be dealing with heights in the future, you can train yourself not to fall into vertigo. But if you don't have opportunities for training down your reactions, not looking down is the next best thing.
Let's just be clear. You are very near equivocating on rational. There are two basic definitions, though it may be natural to add more for some reason. Essentially what you are pointing out is that sometimes it's instrumentally rational to be epistemically irrational.
I don't see much of a problem with this. As rationalists, we primarily want to be instrumentally rational. Scratch that, it's the only thing we want (intrinsically). Being epistemically rationally just happens to be the best way to achieve our ends in a large percentage of cases. It also may have a direct component in our utility function, but that's another issue.
There is another definition, one better than either of those two, not only because it is more useful but because it is generally used and recognized.
With sufficiently limited resources, it can be rational (in that sense) to be irrational, if the available resources are sufficiently limited.