help with some maneuver node weirdness when plotting future orbits

[Drew Kerman]

My game captured a small Class-A asteroid that flew by in front of Mun and slowed it down enough to stay within Kerbin's SOI. Sweet! It's a bit far out (63Mm) and its orbit still passes through Mun's SOI so I placed a maneuver node and used the right-click buttons to advance the node around one orbit at a time until it found the next intercept. Then I did it again on the projected path to get a third intercept and see what the asteroid would be up to in the future. Given that it moves closer after the first encounter, that would be a good time to head out, grab it and place it in a more stable orbit.

However a few in-game days later (earth time) when I viewed the rock in the tracking station the saved maneuver node no longer showed any Mun encounter. So I hopped over to the rock (the latest Kerbal Alarm Clock lets you jump to the asteroid when an alarm for it fires, so set a 0 second delay, hit Jump to Ship and boom, you're in flight with the asteroid) and deleted the node, made a new one and proceeded to advance my orbit until Mun encounter. This is what I got:

the orbits are different and now instead of 107 days it's 196 days to AP after the first encounter. Uhm, okay. I deleted that node and tried again.

son of a... 300 days?? So I created a second node on the projected orbit and that changed the Ap from 69Mm to 68Mm

Then, if I grabbed and just moved the node around the orbit back and forth, it would change the orbit until after dragging it around for a bit (and through a Minmus encounter) I ended up with this - although I could have kept going

Then I tried moving the node ahead 1 orbit with the right-click buttons and doing so also moved the node's position and the orbit

And deleting the second node left me with this

Then I restarted the game and got this

I restarted again and the same result as above came up.

So, if the physics is supposed to be on rails for this kind of stuff what's messing with the placement of the orbits? Or am I misunderstanding how KSP plots this stuff?