Looking at this the other way, you need to understand why steam technology was eventually outmoded by internal combustion engines and electric engines between @ the 1880's and the 1920's (like most things, supplementing older technologies takes time).
The first issue with steam is that the power to weight ratio is generally lower than with competing systems. Since steam is an external combustion system, you need the extra mass of boilers, steam pipes, condensers (if fitted) and so on to extract the chemical energy of the fuel into mechanical energy. Internal combustion engines (Otto, Diesel and Brayton cycle) all dispense with the intermediate step, so engine machinery is much lighter and more compact.
This scaling effect works downwards rather than upwards. Large steam powered systems continued to dominate in locomotive engines and ships into the 1920's and even into the Second World War (many ships were powered by "triple expansion engines", for example), and thermal generators are still dominated by steam generation whether coal, oil or even nuclear powered. On a very large scale, steam is still competitive.
The second issue with steampunk is flexibility. Since steam is generally competitive when you are looking at large systems, then you are tied to the location of the steam engine, rather than being able to move around as needed. Factories in the steam age use a single large steam engine which drove a series of drive shafts along the ceiling. Pulleys attached to the drive shafts drove belts or chains down to the machines below. You could imagine a computer server room filled with mechanical "Babbage Engines" all running off a locomotive sized engine in the back, but this technology, like others, isn't going to scale into PC's, laptops or tablets (the idea of a person carrying a scoop of coal for their laptop, adjusting the chimney for the correct draft and waiting for the boiler to come up to pressure for a laptop Babbage machine should give you some idea of where this is going.
To actually make a steampunk society, you would need to jump-start steam technology by several decades. Very simple steam and atmospheric engines were invented as far back as the 1rst century AD, but Roman society generally thought of these devices as toys. What we understand as steam engines were invented in the early 1700's, so your point of departure will be to commercialize steam technology and improve it before James Watt's condensing engines were introduced in 1781. Perhaps James can be born several decades earlier, or Newcomen's engine introduced in the 1690's and a budding genius develops the condensing engine (which was far more fuel efficient) in the early 1700's.
The point is to give Steam engines such an entrenched advantage in terms of sunk costs, developed infrastructure and the huge mass of technicians and other trained workers needed to keep steam power viable that competing technologies will find it harder (although not impossible) to break into the market. The widespread availability of stem power and the costs of conversion would allow for a much longer time-frame for steam to be viable, and for steam engineers to develop cost effective responses to internal combustion and electric power (steam cars and even steam airplanes were developed, so it is possible to have a Steampunk age lasting perhaps from the 1700's to the 1950's in your timeline).
