The greatest weakness of any sort of "Robot Overlord" is mathematics; specifically Chaos theory and what is known as the Local Knowledge Problem.
Chaos theory suggests that in large complex systems (weather, ecosystems economies, societies) inputs and outputs are not linear, and outputs can be disconnected both spatially and temporally (the decision you make now does not have an effect until some later date, and the effect occurs in a different city). This is amplified with larger systems, as the number of interconnections rises almost exponentially as the number of connections rise linearly:
In any network there are (k * k-1) unique ordered pairs of actors (that is AB is different from BA, and leaving aside self-ties), where k is the number of actors. You may wish to verify this for yourself with some small networks. So, in our network of 10 actors, with directed data, there are 90 logically possible relationships. If we had undirected, or symmetric ties, the number would be 45, since the relationship AB would be the same as BA. The number of logically possible relationships then grows exponentially as the number of actors increases linearly. It follows from this that the range of logically possible social structures increases (or, by one definition, "complexity" increases) exponentially with size.
So the Robot overlord would have to control the variables and interconnections between 7 billion human beings, as well as hundreds of millions of economic, social, political and other organizational units, plus outside variables like weather, natural disasters and random events, which are all interacting continuously. Introducing random events in this vast matrix could be as simple as drawing up a table of "inputs" and picking one by rolling a set of dice. Most of "your" random inputs will be drowned out by the noise in the system, but once enough members of the "underground" started doing this, second and third order events resulting from these activities will become apparent, and provoke further actions and outcomes by other actors, which were not anticipated by the Robot overlord.
The other mathematical issue is the "Local Knowledge Problem". Since information is diffused among any large system, local actors are better placed to see and act on this information than centralized hierarchical or bureaucratic systems (which is what the Robot overlord really is, just orders of magnitude faster than the Post Office or Department of Motor Vehicles). Even without active opposition, the robot overlord needs finite time to accept inputs, process them, make a decision and then send instructions back down to the field. During this time, the conditions observed at time "x" will have changed somewhat, and the resulting instructions on how to deal with the issue will be slightly off, based on outdated information. A new set of observations is then made, and the cycle repeats, with cumulative errors accumulating at an ever increasing rate (and don't forget point one, the effects of the incorrect instructions might provoke effects that are spatially and temporally remote; solving a problem in Brazil causes an economic spike in a Japanese company, which causes troubles in a school in Ukraine....). Active opposition increases the problem by feeding incorrect inputs or sub optimally executing instructions, making the feedback loop worse rather than better.
So even in theory, a Robot overlord is actually impossible. A sufficiently powerful computer system might be able to impose its will upon us, but will need powerful coercive measures to continue as increasingly sub optimal outputs occur (everything from an actual police force to a "Ministry of Truth" that feeds false but comforting information to the masses). The fate of the Soviet Union should be illustrative; they had an iron hand over virtually every aspect of life and production in the USSR for 70 years, but in the end the state virtually evaporated with the "Fall of the Wall" and the dissolution of the USSR a few years later.
A Robot overlord state might decay internally in a slow fashion without outside challenge, but eventually will become so brittle and inflexible that an unexpected "challenge" (maybe a natural disaster or crop failure) will create the breaking stress. With internal challengers and active opposition eating away at the data structure, the day of reckoning will come sooner rather than later.