Not necessarily, though it is possible.
As you say, most people are specialised. But given how just how specialised many people are, this begs the question how we make our current technology. For example, look at supercomputers (or even normal computers). Look at vehicle production. These processes aren't done with just one person operating everything, nor with one discipline of people. Computer manufacture involves people who understand processor architecture, OS designers, materials specialists, screen makers, precision robotics, and of course, engineers to make sure all the machines work. Car manufacture is similar: although it is mainly robotised today, the robots need maintenance, and someone has to design the car in the first place.
None of these people can do all the jobs in the factory. So, the point is, for complicated jobs you get a group of people together and they do the job by working with each other.
In the future, we may well have far more complex technology. I think that as this happens, the teams we will need to work the processes and machines will grow, and the fields they each study will narrow. So, in theory there definitely is a limit: where there are not enough people to fill all the required roles.
However, it is entirely possible that among our new technology there will be advanced AI and computer memory. We may end up being able to build robots and upload all the necessary information for them to do many jobs for us. This would end up with everyone being employed in robotics manufacturing, until we build robots to do that at least.
So yes, there is definitely a point where this will happen. However, if our technology advances at the right rate then we may be able to save it by building helpers.