The solution was not military, the solution in Vietnam is never military, especially in the North. That's why the French first didn't try and then lost when they tried, and that's why the American lost. You cannot militarily conquer a country with so many jungles and mountains if you don't have the support of the population. You could try to break them but a) that'd be akin to genocide in the North and b) the South would make Erithrea a paradise in comparison as your population would be working against you.
As
@Meordal eloquently explained, there was a massive fear of the communists in Vietnam, which the French used extensively. If anybody else had been standing, the communists shouldn't have been able to touch power with a ten foot pole.
But the French pushed everybody to the extreme and the Japanese purposefully sowed the seeds of maximum chaos after they left, hence the communists. But even then, many people hated the communists almost as much as the colonisers, which is why you have two countries in the first place.
The communists were opposed by the Catholics, the Buddhists, the Cao Dai, the business class, the bourgeoisie...
But Diem went with crushing everyone who wasn't Catholic. If he hadn't been that fervent, or more balanced in it, he could have gathered the support of other religious groups, which could have given him more support in the rural population.
No, or less, support in the South, and you can fully utilise your resources and actually try to take the North, if anything by getting refugees and taking the manpower away from the North, like in East Berlin.
In that situation, besides his own political skills, Diệm had to trust in his relatives, the catholic minority and the backing of his American supporters to overcome the obstacles and neutralize his opponents. Diệm's favoritism towards Catholics and persecution of South Vietnam's Buddhist majority led to the "Buddhist crisis" of 1963. The violence damaged relations with the United States and other previously sympathetic countries, and his regime quickly lost favour with the leadership of the Army of the Republic of Vietnam.
- Failed land reform
- Catholic minority in power
- Dependency on French and US aid (versus nationalism)
- National war fatigue
- Corruption due to factionalism and family connections
- Viêt Minh national ideology common to many citizens
- The wish to reunite the country in the hearts of all citizens
- Future junta leaders who assassinated him in his own government
- "Pro-communist" junta leaders : communist agents (or former Viet-Minh)
- Lack of international or US reactions against the coup, leading to more coups
- Destruction of the traditional anti-communist factions and social structures