Unless there is some drastic change in how the economy works, I doubt that slavery will ever be profitable again.
Slavery works best in situations where one has work a great deal of work to that does not require many job skills, is repetitive, very labor intensive, fast to learn, and easy to monitor.
While there was a vast need for that sort of work prior to the industrialization of the agrainian economy, it is really not needed any more. Decades ago, large farmers and ranchers needed dozens, or even hundreds of hands to do the work of preparing, plowing, weeding, harvesting, preserving, and distributing food. However, with modern technology, farms spanning hundreds of acres can often be productive with just a few people.
The real problem with slavery is that the slaves tend not to be motivated. Slaves quickly find out that if they do more work, then more work will always be expected of them, and that no matter how much work they do, there will be almost no chance of them ever getting a fair share of the profits. Therefore, slaves usually do just enough work to satiate their owner and any more.
However, in a modern society, one needs workers that are well trained, highly motivated, and can function reliably with little supervision. In this case, the workers know that, in most cases anyway, that the more they help their organization, the more the company will pay them.