How to ‘Test BACC “Thumper” Solid Fuel Booster in flight over Kerbin’

While you can't undo an end flight (well, at least not without a stringent backup policy), you can prevent yourself from accidentally clicking the end flight button (and then confirming said action) with this mod. Of course, even this isn't fool-safe, as you have to enable the option to begin with. Also, there is the possibility that it will get disabled if you start undocking parts. With my brief testing, it looks like if one piece of a station was set to block end flight, the entire station will block as well.

Previous answer kept for posterity. The game mechanics for ending a flight were drastically changed in version 0.21 such that it's much harder to do accidentally. Yes, it's possible to revert the state of a flight to an earlier point (a quick-save, the launch, or the VAB/SPH), but this is much less destructive compared to ending a flight.

You can still end a flight from the tracking station (by "recovering" vessels that have landed on Kerbin or "terminating" others), but since this is a much more deliberate action, it's less likely that you'll end a critical flight accidentally.

Kerbals can't die for any other reason than lithobraking (just like aerobraking, only difference is that you replace the atmosphere with the ground) and a collision with an object.

When you're in control of the command module, try switching to Neil by using the [ and ] keys. Unless there's a lot of debris near by, it should only switch between the module, flag and any kerbals on EVA.

If taking control of Neil doesn't work while you are in control of another object, you can go back to the space center and enter the tracking station. There you will be able to select your kerbal from the list on the left and press the "Fly" button.

The only thing that could prevent you from taking control of that poor kerbal is a bug.

In this case, basic troubleshooting. Reload your save file. If that fails, restart the game. If this fails, well, assume that Neil met the kraken.

You could also try bumping him so some of its variables in the code are changed.

If all fail, well, roleplay it. He died of hunger while you pressed the big red button in the tracking station.