With the exception of a very few niche designs (1895 Nagant, for example), revolvers don't have a gas seal between the barrel and cylinder. That means that hot gas is going to be expelled out around the front of the cylinder after every shot - not a major problem on handguns, as your hand normally shouldn't be anywhere near that anyways - but with a rifle, it becomes a problem as the shooter's forearm is going to be extending past the cylinder.

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Pressures were also a major concern. Revolver cylinders tend to have fairly narrow chamber walls, which they generally can get away with by virtue of using low-pressure pistol cartridges. But rifle cartridges were significantly higher pressure - 45 Colt, for example, maxes out at 14,000 psi, while 45-70 government (the standard cartridge of the US Army until the adoption of 30-40 Krag) had pressures maxing out at 28,000 psi. When we get to smokeless powder cartridges, the pressures get even larger - WW1-vintage 30-06 ran at about 50,000 psi, while even modern .45 ACP has a max allowable pressure of 21,000 psi. What this all means is that a chamber is going to need to be significantly stronger for a rifle cartridge versus a pistol cartridge. That means a larger, sturdier cylinder and frame, and it'd likely preclude a lot of the weaker configurations that were popular in early revolvers (mainly top-break designs, which already have been phased out in handguns due to their weaknesses). Compared to a more traditional magazine-fed rifle, it's going to be a heavy affair, as you've got to have multiple chambers as strong as the single chamber on a more traditional design.

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There were also issues with institutional inertia within various militaries. Magazine-fed rifles in general took surprisingly long to catch on, largely thanks to logistical concerns, and thus it took until just before the advent of smokeless powder for magazine fed rifles to really catch on as a standard military small arm. Even then, many major powers included magazine cutoffs in their service rifles specifically over fears of undisciplined troops firing too fast in a panic.