Top-break revolvers have three primary disadvantages over solid-frame revolvers: they are not as strong, they are more difficult to engineer with complete extraction of longer cases, and they are more complex and expensive to manufacture.
As to strength, while they are weaker than solid-frame guns, they're historically more than adequate for the relatively low-powered cartridges they're chambered for. Cartridges like .22 Long Rifle, .38 S&W, and even .44 Russian and .455 Webley simply aren't all that hard on revolvers because they are low pressure and fairly mild-recoiling for the size guns they're usually put in.
Also, not all top-break revolvers are equal in strength. Probably the majority of top-breaks floating around today are small, inexpensive pocket guns from makers like Harrington & Richardson, Iver Johnson, Hopkins & Allen, Forehand & Wadsworth, and others. These guns, while still better than some of the cheap semi-autos like Jennings, Bryco, and Davis, were meant to be carried much more than fired and were not made with price being of higher concern than durability. The best quality top-breaks are probably the S&W's and replicas thereof and the higher-end British models like Pryse, Webley, and Enfield. The Webleys and Enfields in particular were probably the best and strongest top-breaks ever made. Not only were these guns made from better materials, but their stirrup-type latch is stronger and greatly superior to the more common eye-latch of most other top-break revolvers. If you wanted the most robust top-break available, the Webley Mk. VI would probably be the way to go.
The second issue is that a top-break is more difficult to design for complete extraction of longer cases like .38 Special and .44 Special, much less even longer cartridges like .357 and .44 Magnum. This is because the mechanism for automatic extraction must all be fit into a fairly confined space. With a solid-frame revolver, the only limiting factor as far as extraction is concerned is the length of the ejector rod and, therefore, the length of the barrel against which it lies.
Finally, a top-break is simply more complicated and expensive to manufacture. The top-break design, particularly one with automatic extraction, requires more complex machining and has more small, moving parts. This is why a Uberti Schofield replica costs several hundred dollars more than a comparable Single Action Army or Remington Model 1875/1892 replica does.
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