Even a 0,1 m/s difference in speed makes a difference over the years. The only way to ensure that they stay in their position is to fiddle with their orbits in the save game file.
Note that this only works as long the satellites remain in their on rails-simulation, so you can't directly control them by using the control center. Otherwise they will always drift.
You might find these links helpful, there are lots of tutorials how to do this:
Scott Manley's video tutorial
Orbits in KSP wiki
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.
Best Answer
There's a bug/feature that causes excessive lag when you're close to the oceans. This is because the oceans are actually loaded as a separate planet entity. So the only way around this is when this bug is fixed, or you try running the game with a more powerfull computer.