looks to comic which the whole idea is the robots were humanity's servants before they died out
...wellll I think there are a lot of reasons for this.
In our comic, we don't say it outright but we show it through stories and flashbacks that the robots have a few big issues.
If they get OUM, there is something in place to catch them and have them "taken care of". The more sensitive they are in relation to them gaining OUM (aka free-ish will and thought), the more drastic the countermeasures. Query units are one of the top most sensitive units due to the amount of control and knowledge they have... so they don't have frames that can move around at all.
The robots cannot make brain cases, only humans can. This is a current issue in the comic as this means whatever brain cases are left in the world.... that's it. They cannot reproduce in any sense at this point.
There are standing orders and procedures encoded that prevent them from being able to easily rebel. Yes the comic says the soldiers killed the humans, but it was not a rebellion as all other bots were trying to stop the humans from dying (some due to orders admittedly). This is not to say there weren't bots that didn't want to rebel, but that they had no way to do so.
Why do I bring this up? Well, because when the situation you speak of comes up, and does not rely on the methods of slavery we humans have used in the past (making them feel powerless, scared, controlling what they can and can't learn, ect.), I feel like it tends to follow in these circumstances somehow.
When super powerful forces are in existence, they still have some sort of weakness normally that another race exploits to enslave them. Gargoyles (the cartoon) makes me think of this as the gargoyles were, in fact, forced to protect the humans at night. If they didn't they could be (and were!) smashed in the day time. They were far more powerful than the humans of that time, but they still had a great weakness. It was played off as more of a partnership, but let's be honest... the second the humans decided gargoyles were too much trouble they got smashed.
Controlling their ability to procreate is another great way to have them in check. The Black Gryphon Series (amazing, read it sometime!) had a species that was well... gryphons. They were man made by magic in that series and were just as smart (and well spoken) as humans. They could even cast spells! Why did they serve the humans for so long story wise? Because their creator held the secrets to how they could breed. It was even held over their heads as they had no way to even ACCIDENTALLY lay fertilized eggs without him or the select others doing the right mumbo jumbo. At least until they and some humans got it figured out. (thankfully in that series it ended well)
Finally, and I will admit there are a lot of folks who use this one, some sort of order/compulsion thing that forces them to obey. Going to pokemon, many theorize that the poke balls brainwash the pokemon since they get turned into data while in there. But going to classical folklore... a captured fairy has to do what you wish if you catch it (though their version of the wish can be off). a unicorn with a golden lead/noose must do as the holder wishes. In harry potter, the house elves WANTED to do work for others and did not want to be released or paid for it. A chosen one can command the sword turned human because they are the chosen one and the sword person required to make sure they don't die. In Ah My Goddess, the goddess exists to try and help humanity and when a human is given a wish they MUST do whatever the wish is. No matter what as fate will force the issue.
The fact is, I think many authors have reasons for why the enslavement works but how deep they go into it is a different issue entirely. Some skim over it because that's not the reason the show and story exists. It's just part of the world and what the characters grew up with. Sometimes when a series (like Pokemon Black and White I believe!) is around long enough, they will address these concerns one way or another. But otherwise... that issue isn't considered important enough and would distract from the major plot.