well ... to figure out if it was doomed as said, you'd have to figure out why it collapsed in the first place
While overreaching Generals is a good answer i think its imprecise.
The Late Roman Republic was a empire effectively ruled by some 300 people (if that many) controlling each their little patronage (either direct or through family relations), while for the most part sitting in the senate (while perhaps 'owning' some other senators) and using their vassals and deep coffers to turn the elections into a parody of itself ... These few people rules over a country many thousand times bigger than them, hence from the Marian Reforms and onwards the only way to make a grab for any kind of power for those outside the elite would be through military or brilliant financial know-how (which again needs a good amount of seed money).
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So the problem is (at least) 2 fold
Roman republic is ruled by a political structure created (with hardly if any change in setup) to rule a city state, multitudes smaller -> high protential for civil revolts/wars against the ruling elite ... specially from sides that see the republic as a conquering overlord that have little or no concerns for the wants/needs of their vassals (Italian Socii's).
Marian reforms, and the following wars showed entrepreneuring military generals with visions of grandeur a way to gain supreme power.
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There are several ways this could be handled making the republic more likely to survive.
1. Instead of a rigid political structure that neither bend or moves a inch, make it a more including structure with 'regular' inclusion of new territories (exact way how I don't know ... Gracchus might be the last good shot at this that won't be to little, to late)
2. A want from the senate to actually make the soldiers like them, instead of moaning about that the generals fight a major political battle to get them a decent pay (Marius ideas for settling soldiers in conquered territories as a nationwide plan might do it, instead of forcing all generals to fight for their soldiers, hence putting them in 'debt' to their general instead of the senate)
3. Selecting generals out from a "talent, not birthright", weeding out the couch generals 'that believe they can (and should) control an army when they would be unable to organize a trip to the whorehouse' might help them out quite a bit, perhaps even to the degree that the Marian reforms aren't needed in the first place, and so that the Socii aren't as annoyed by roman disrespect/lack of caring about keeping their troops alive ...