When your project seems to be running on empty, you have to ask yourself -- what are the firm employees doing? If the answer is "not showing up anymore" or "bailing to other projects the firm has," then maybe you should consider other employment options.
Yesterday, one of the staff attorneys for one of the firms on this project was in the room in which I am seated (I decline to say "in which I am working," because that hasn't been true since November). Other temps in the room were asking him stuff, mostly not work related (which I would never do -- I don't give a fuck about anything not work related with respect to a firm attorney. It has no bearing on my employment and, thus, on my life, so I don't care.) What he said was useful, but did not surprise me, and so not asking him did not deprive me of information I needed. What he said was, "I should probably try to get on another case." No shit, Sherlock. There is no work on this case, and hasn't been for more than six weeks. As a firm employee, he needs to keep his billable hours up. Staying on this case isn't doing that, and what he said confirms that billable hours aren't on the horizon. That means it is time to get out.
That, of course, is why I have been applying to every project with either a higher hourly rate or more hours. While this project might not die for a while, it apparently is not going to get better, either. I can't live on 40 hours, so it is past time to beat feet. On it. This swordfish might not be dead, but it might as well be.