In the end, the major limit of automation is peak oil, together with the general threat of a resource crunch.
I would argue you can have automation even after the "cheap oil" peak.
It will just be more expensive getting the energy for automation. Let me elaborate :
An average adult uses about 2,400 calories in a day. That is roughly 3 kwh.
Now, assuming we use solar AND that machines have 1/4 the efficiency of the human body, in energy terms you will need 12 kwh to replace a human being. Since the cost of 1 kwh using solar is 0.25 this means you need 3 dollars to replace a human being ( in energy terms ). The equivalent is about $5,000 in solar panels plus converters , wiring and batteries for a total of $15,000.
So anyone willing to do a job for less than $3 a day will still be employed automation notwithstanding.