If you are working on something the people deciding on the size of your paycheck want to kill, time to find a new project or a new company. Why fight a battle you're sure to lose?
I've also seen people make careers out of taking over projects cut for the above reasons as customers still demand support. I've seen many downturns where my project was important enough to not be cut.
I've seen many downturns where my project had massive cuts, but I personally was not the person cut. Most often projects are not killed outright, instead they go through a long down spiral (not always, but typically) and you can make a lot of money being the expert on a product that is making money if you are able to hang on. Someone needs to leave as there isn't the budget to pay everyone, but that someone need not be you. Often these projects pay very nicely for working 9-5 with no pressure to do overtime.
I know this may appear so but the signs are there. We only want this to be true so we do not see it.
I've been in a similar situation where all we were seeing was high pressure to deliver something. This made it appear that is because the project is important. But the underlying reason was that if we didn't, the project would be dropped. Which they did.
A project may be critical but even more so is to be in a certain time frame and budget, otherwise the project doesn't have a reason to exist any more. But until that moment is still very important because, at the very least because there was a lot of investment into it.