Psychologically speaking, the phenomenon you describe could be called "cognitive dissonance."
Cognitive dissonance is experienced by a person who has two conflicting thoughts in his or her mind at the same time, each of which is struggling to be recognized and dealt with.
It has been said that you can't believe you are crazy and, at the same time, not crazy, without feeling some dissonance, or to use a more familiar term, discomfort. What do you do then? You choose one or the other (crazy or not crazy) and begin to come up with reasons why you are one or the other (the term for this is "clustering").
Some people struggle very little with cognitive dissonance. I guess you could say they are "dissonance tolerant." Other people, however, are very much "dissonance intolerant," and they seek to resolve that dissonance by deciding, by making a choice. (From your description of the self-deluded person whom you describe, I take it she or he is not yet ready to make a decision as to how badly things are really going!)
As for people who are dissonance tolerant (or sensitive) and are therefore eager to admit, for example, that they are wrong and need to go in a different direction, the dissonance that would be created and aggravated by NOT admitting things are indeed going badly is simply untenable and would cause them too much pain. They therefore make a dissonance-resolving decision. In other words, they come to the following conclusion:
"Looks like we'd better 'cut our losses' and start over again. As things stand now, that would be the only sensible thing to do."
On the other hand, as for people who are dissonance intolerant (or insensitive), they are perhaps not that driven to resolve the dissonance, for whatever reason(s). They might say to themselves,
"Meh. We've come this far. We may as well take it to its conclusion, regardless of how inadvisable some people say that would be."
I suggest that we take one or the other approach at different times in our lives, depending on our circumstances. Perhaps we're all dissonance sensitive (or insensitive, as the case may be), but in differing degrees and in different situations.
Perhaps a "real-life" example would help. Let's take a compulsive, degenerate gambler. Upon losing again (and again and again), he deals with whatever dissonance he experiences by continuing to gamble, to a point where he gambles away a fortune. In other words, he's dissonance insensitive. Who knows, maybe his dissonance insensitivity itself is his "payoff"--the "juice," as it were, which keeps him digging deeper and deeper still, the hole into which he has fallen.
On the other hand, for the occasional gambler who is dissonance sensitive, upon losing a few bucks she throws in the towel and says, "Oh well, maybe next time I'll do better," and that's that. That little bit of dissonance triggered by losing a few bucks causes her to call it quits. Consequently, maybe around the same time next year she'll give gambling another whirl, and if she loses, no big deal, but if she wins, that too is no big deal.
Hey, we all deal with dissonance in different ways. How we do so may have ethical and/or moral implications, depending on our circumstances.