The first question to pose is why Mexico succumbed to a dictatorship and didn't achieve a liberal-democratic regime, since this is what most liberal politicians claimed they wanted. The answer, I think, has two sides to it: .
(1) No representative political institutions were created by liberalism at local level. The regional caudillos remained firmly in control, and what Mexico had in the way of state institutions' were concentrated still in Mexico City. The liberal leadership simply joined the ranks of the existing landed oligarchy. .
(2) The totally urban-based liberal political movement had done nothing to bring the agrarian masses into any form of participation in national life: indeed, liberalism created new types of rural unrest. .
This second point is, I think, particularly important. In the early decades of Independence, as we've seen, the different political factions in Mexico tended to unite in the face of fear of popular rebellion and inter-class conflict. Those who were inclined to liberalism were too scared to rock the boat. The constitutional republican state created by the liberals left private class power not simply untouched, but absolutely rampant. The only problem was that it was so weak and ineffective that it could not guarantee internal social tranquility or do anything about Mexico's national' problems - in particular the continuing threat posed by the USA to the country's national integrity.
diaz's regime offered an end to civil wars, greater social stability, and promised a form of national development: from the ruling class point of view it probably didn't matter too much that this national development involved the increasing domination of foreign capital initially, since the major problem through the 19th century had been the loss of national territory to the USA, and securing effective domination over the lower classes.