I disagree with assessment given by Chad in another answer. Management is not infallible. Certain direction may not be feasible, and to simply accept it because the decision has already been made is tantamount to agreeing with the decision. If the river forks, and you know which direction is pointed at the Impending Waterfall of Awful Doom, it does you no good whatsoever to complain that you advised the other fork once you're already flying off the ledge.
This comment is a bit closer to it, I think. The first thing I would advise, is strike the word "fight" from your vocabulary. The idea is conflict resolution, not instigation. Chad is correct in that if your direct manager is a lame duck, your options are terribly limited. But that doesn't leave you powerless.
I don't generally care to involve HR in these types of scenarios, but that is one option, by way of pure CYA. "I'm terribly concerned about the direction we're taking on this project, and I've voiced that concern to no effect. I just want it listed for the record that should the project fall short of its objectives, I provided alternative solutions that may have diverted that outcome."
Another option is to document as thoroughly as you can your predictions for the project, and the potential alternatives to management's chosen course of action. Losing a key member is easy enough to quantify; "The project requires x skillsets and x amount of time to complete. We are commencing development with x skillsets and x headcount." Math is rather incontrovertible. A bit more difficult to define is:
serious network issues which is impacting [work]
Still, documentation is your friend. Report to your manager, in email, what you are experiencing and its direct effect on the project. Provide a feasible solution, if you can, and ask for direction on how best to proceed. Neither of these are any more complicated than open communication.
Recognize that every problem presents an opportunity. Don't just point out what's wrong... offer solutions. "It's unfortunate for the project that person X is being reallocated, but if we can expend some effort on resolving Y's network issues, we may be able to offset the impact of losing X."
As a manager, I will often turn to my team with project hurdles and ask them to help me determine a resolution, because I know that my team is entrenched in the technology and may know something that I don't. Sometimes it's just for a different set of eyes, or a sounding board, and sometimes just to let them know that I'm aware of their pain points, and that we're all in it together. Perhaps your manager employs a different tactic, but I can pretty much promise you that if you provide him with enough ammunition to correct course, everybody will thank you.
I do agree with Chad that you should give it your best effort. You may not be properly lauded for being a team player in the face of adversity, but at least you'll have the peace of mind that you were not one of the people throwing up their hands and crying "Who's John Galt?"
Finally, be prepared for the possibility that perhaps it can't be solved. The course may already be set and all you can do at this point is hand out life preservers. I've worked places where something had to fail in spectacular fashion before senior leadership recognized it as an issue; if that's the position you're in, then all you can is to continue to communicate your concerns.
Don't fight it. Solve it. And if it's truly unsolvable (which I am unlikely to concede), provide regular, honest and professional updates of how the project is progressing. "Sir, we're headed towards the waterfall... Once we pass that boulder ahead, there's no turning back... We just passed the boulder, should we start assessing who in the boat knows CPR?" At worst, nobody can cry surprise when you're going over the waterfall, and they won't be able to point the finger at you for it.
Perhaps you'll find empty consolation saying "I told you so!" :D
