The size of the "court" is one limiting factor: a medieval monarch's court was small enough to reasonably travel with him and set up temporary lodging and offices at any of a number of places throughout the country. But once governments start growing to anything like modern size, the scale of office space and lodging required becomes prohibitive, as does the logistics of moving that many people around. Not to mention all the paper records that would also need to accompany the travelling bureaucracy. You could leave the bureaucrats back home in a permanent administrative capital, while the King (or President, or whoever) and their council or cabinet and their respective staffs continue to travel, but before telegraphs and telephones, that means that the King and his council are only able to very loosely supervise the bureaucracy.
Another limiting factor is that as the economy becomes more complex and the scope of the government's involvement with the economy expands, you get an ecosystem of lobbyists and petitioners who are going to need regular contact with the government. If your business regularly needs permits, regulatory rulings, tax filings and appeals, customs approvals, etc to operate, then it's going to be really inconvenient for you to juggle running your business in London while simultaneously chasing the government as it travels around the Midlands.
Infrastructure is another potential problem. If you look at railway maps of European countries, especially older maps from the 19th century, you'll see that most of them start out with lines radiating out from the capital with cross-connections between the spokes only being set up later. The centralized hub has a huge advantage as an administrative center, both because the capital can communicate with the rest of the countries faster, and because of the advantages of having your commercial hub and administrative capital be within reasonable proximity of each other. This issue is easiest to illustrate with railways, but it's also a factor in road and canal systems in the pre-railway era.
I think infrastructure is the least inevitable bottleneck of the three, since 1) cross-connections and secondary hubs did get added, and 2)
some countries had decentralized railway networks even during the mid 19th century.
So to answer your question, I think itinerant capitals become difficult around the late Renaissance, then very difficult with advent of the industrial revolution. During the 20th and 21st centuries, the bottlenecks start to ease: as transport networks fill in, telephones, telegraphs, and faxes become widespread, and especially as records are computerized and the internet makes long-distance communication and collaboration even easier. But by then, countries have already paid the cost of a fixed capital (permanent office space, inducing the workforce to move to the capital and its suburbs, etc) and the assumption of a fixed capital is baked into processes and institutional culture, so you'd need a really compelling reason to decentralize or itineratize the government.