Treat your Skull with Respect
or: the Narrative Answer
So you have an adorable flying robot skull that does whatever you tell it to do, no matter how unpleasant or dangerous, with no complaints or questions. And now it seems to be thinking for itself...
All of this ties closely into a lot of fairly common themes in science fiction - particularly the pulp science fiction that is WH40k's lifeblood - about artificial intelligence, creations rebelling against their creators, the perils of bringing a dead comrade back to life, intelligent robots slowly becoming unwilling to continue serving simply as tools for humans, etc. These things happen in fiction because they're interesting places to take the story; once you have robots, a robot rebellion is a natural story waiting to happen.
I can only presume that part of the reason that the GM is considering having your servo-skull start becoming independent, acting more and more unpredictably, and potentially rebelling against you is because, well, the story that would result would probably be pretty cool. You said it yourself:
We had some fun coming up with situations of the Servo Skull (Eli) becoming independent from me and quite simply vanishing [...]
In general if something seems fun to speculate about potentially happening in game it would be pretty fun to have happen - in this case, it's not only fun, it's also one of the most natural places the story could go.
If you (out-of-character) don't want your own skull to turn against you, you need to make it possible for there to be an alternate story path that is a more natural progression of the story and also pretty fun. How exactly you do that is a matter for your own creative vision. But every possible direction I can think of revolves around treating the skull as a character in its own right, giving that character actual in-character reasons not to rebel and making your interactions with that character interesting or fun for some reason.
By way of example
The idea - and don't feel even slightly bound by this, it's merely a suggestion - that immediately springs to mind is having your character, already a little bit insane, start talking to the skull as if it were (drawing from your linked question) actually his old friend Eli. Reminisce over that time with the stuff on that one planet, ask for advice in Eli's area of expertise, occasionally tell Eli that you're really sorry you got him killed. If you did this, suddenly "your skull rebels and runs away" is fun, but not as fun as "the skull represents your character's guilt over Eli's death" - and since you treat the skull with a modicum of respect, it running away is a less natural story path than it sticking around, interacting with your character and actually beginning to take on more and more aspects of Eli's personality.
Talk to your GM
or: the Social Answer
Your GM seems to possibly find the idea fun and interesting. If you also like the idea of your character's skull rebelling against him, and you're looking for a purely in-character solution for what your character would plausibly try to do to prevent this, read no further.
Otherwise, if your character's skull running away is something you don't want, OOC or IC, discuss it with your GM. It almost goes without saying that this should be a calm and non-accusatory discussion, and you should bring with you the understanding that sometimes, in an RPG, things will happen to your character that you don't want, and that's okay. But if you think that your character's skull running away would not be fun, or it would be less fun that an alternative idea you have, or you'd prefer the game to be less on the side of transhumanist exploration of the rights of AI constructs and more on the side of blowing things up and smoking cigars, or, well, whatever reason that leads you to believe, out-of-character, that the GM taking your character's skull away would be a bad idea, then you should probably at least discuss your reasoning.
If you have a decent GM, they'll take your concerns on board, address those they can and tell you how they may have changed their mind about their future plans (while attempting to avoid spoiling anything).
