Sorry. I shouldn't have been so vehement last night with my words.
A lot of how I imagine the respawn system to work relates to my personal job--managing servers and websites. With these items, you always have back-up locations, development environments, and scheduled back-ups for any databases related to those environments. Since I'm in an environment that focuses so much on preventing total collapse, it's frustrating to me to see people writing about environments where negligence causes a catastrophe.
I do share some similar headcanons with >>12605. I do believe that if such a machine existed, it would have to be able to recycle parts from a deceased individual. I also think that there would have to be a database to store missing gaps and parts that are destroyed beyond repair (i.e. gibbing, missing atoms.) If you had this data system, you'd also want to update it with new statistics and changes in body structure from day to day to allow people to become stronger and fight better. (Of course, accidents happen--look at the Sniper's scar.)
There may be up several respawn machines operating at any given time. Both Mann brothers have one a piece just to themselves. BLU and RED each have one. The Administrator and her staff may have one in case of mutiny (and hey, it might happen.) There would most likely be a dev environment to experiment with various genetic codes and structures as well. This environment is probably what could create class derivatives (genetic mixes, splices, vivisection, etc). There many be other devices to which data is stored; most like some kind of glorified floppy disk, in this case. It's the 1960s in a screwy dimension. Who knows?
I'm not sure how mental transference or soul catching or what have you would work, however. I can't pseudo-science my way into understanding that, outside of traits and experiences being stored in some fashion. Even a huge genetic structure would be easier to store than that.
It's possible to still wipe all of that out, given a large enough EMP that could go through several states. It's just very unlikely. I just have difficulties believing someone would flip a switch, turn respawn off, and then whoops! Permadead teammate. If that were the case, they probably would have killed each other permanently the first night they went to sleep.
Of course, knowing how screwy the TF2 world is, the respawn machine could be something as simple as stapling a Ouija board to a Turing machine. What the hell. Who knows?
So, to summarize my rambling--I have difficulties with "respawn is down" stories because I'm paid to prevent that from happening in real life. Well, not so much respawn machines, but you get my drift. It's the same reason I loathe so many movies about computer hackers and viruses gone horribly wrong. I just can't stand it when someone designs a system without a sufficient level of complexity or security.
But, hey. People can still feel horribly bad about a death, even if the deceased comes back to life. That is a legitimate and human emotion to have.