Is a war between man and machines a realistic possibility?

Yes, there is some chance of it happening, but I put that chance as infinitesimal.

I agree with Isaac Asimov that people will be scared enough of machines that they demand very strong safeguards. By the time we get to robots building other robots beyond human review, by then I highly doubt they will be organisms that want to commit war.

I want you to think of just how unenlightened war actually is.

These robots wouldn't need resources. They wouldn't have some ideology they need to prove. They may care about us enough to want us to stop hurting each other, and they may defend themselves from attack by us, but both of those do not necessitate mass death or extermination. They wouldn't have aggression that they had to work out or sublimate.

Without all of the reasons humans make war, robots would have no need for that level of organized violence.

I would say the answer is, "not yet." It depends on the future role of robots in combat. So far as I know, at this time they are only used for reconnaissance, like rolling a camera into a building to look for insurgents, etc. If robots are armed in the future, and programmed to kill humans in combat, a programming error or a hacker's sabotage might cause such a robot or robots to attack all humans, and not just enemy soldiers. There would be self-limiting factors though. Robots DO need resources. They need an energy source, like a charging station to recharge their batteries, or replacement batteries. They would need replacement parts for the parts damaged in combat, and ammunition for their weapons. Given how unlikely it would be for errant robots to be able to develop a supply chain, the war would end when the robots either ran out of bullets, ammunition, and/or spare parts.

I think it's not possible, even with artificial intelligence. Or at least very very very unlikely to happen. Why? Only 1 reason: when someone makes a coding, he makes backups, code in a way he can still controle the CPU in case of burnout, or in worst case, just reboot/reset it. Everything on a code isn't "intelligence" even if the program learns, and acts as a person. It's only codes, commands, and you simply erase some of them and the device isn't anything anymore. A device won't ever be able to think (at least with the way it's currently made), and the only thing that can pass through its "mind" are numbers. If you want tech to take over us, you'll need something much more complex than some wires than can sit a "on" and "off" state (equals to the "1" and "0" in binary).
Also, I don't think it's possible for this reason: just imagine if you could module a brain like a program. Change the connections, reboot, or even reset it. You would get a brand new person, or a baby in an adult body.
Well that's exactly what you can do to a device or a program. A program becomes hostile? Reboot it! It starts again? Erase its memory, and then change a bit of its code so it won't make the same mistakes.

The only "plausible" way in my opinion is the way of Avengers with Ultron. Only because they didn't code it, theu can't change its code, they can't shut it down, and more especially, it was not a program in the first place, it was an artifact with a consciousness (which doesn't exist, or isn't discovered yet, in our real world).

Answer of your question had been given in Matrix. Surely it's possible.