I think the objections raised by (e.g.) Unknowns, Lumifer and shminux are basically correct but they aren't (I think) phrased so that they exactly match the scenario OrphanWilde is proposing. Let me try to reduce the impedance mismatch a little.

OrphanWilde's scenario -- where your schedule keeps slipping but even with perfectly rational updating continuing always looks like a win -- is possible. But: it's really weird and I don't think it actually occurs in real life; that is, in reality, the scenarios that most resemble OrphanWilde's are ones in which the updating isn't perfectly rational and you would do well to cut your losses and reflect on your cognitive errors.

What would a real OrphanWilde scenario look like? Something like this.

• You begin a project to (let's say) build a bridge. You think it should be done in six months.
• After four months of work, it's clear that you underestimated and it's now going to take longer. Your new estimate is another six months.
• After another four months, it's now looking like it will take only three months more -- so you're still going to be late, but not very. You no longer trust your prediction abilities, though (you were wrong the last two times), so you adjust your estimate: another six months.
• After another four months, you've slipped further. Your error bars are getting large now, but you get a message from God telling you it'll definitely be done in another six months.
• After another four months, you've lost your faith and now there's probably nothing that could (rationally) convince you to be confident of completion in 6 months. But now you get information indicating that completing the bridge is more valuable than you'd thought. So even though it's likely to be 9 months now, it's still worth it because extra traffic from the new stadium being built on the other side makes the bridge more important.
• After another six months, you're wearily conceding that you've got very little idea how long the bridge is going to take to complete. Maybe a year? But now they're planning a whole new town on the other side of the bridge and you really need it.
• After another nine months, it seems like it might be better just to tell the townspeople to swim if they want to get across. But now you're receiving credible terrorist threats saying that if you cancel the bridge project the Bad Guys are going to blow up half the city. Better carry on, I guess...

What we need here is constant escalation of evidence for timely completion (despite the contrary evidence of the slippage so far) and/or of expected value of completing the project even if it's really late -- perhaps, after enough slippage, this needs to be escalating evidence of the value of pursuing the project even if it's never finished. One can keep that up for a while, but you can see how the escalation had to get more and more extreme.

OrphanWilde, do you envisage any scenario in which a project keeps (rationally) looking worthwhile despite lots of repeated slippages without this sort of drastic escalation? If so, how? If not, isn't this going to be rare enough that we can safely ignore it in favour of the much commoner scenarios where the project keeps looking worthwhile because we're not looking at it rationally?