Rome lost a number of hoplite armies vs. invading barbarians and in their own attempts to subjugate neighbors like the Samnites. They were handled roughly by the Samnites at times. The fighting vs. Samnites was often on rugged terrain unsuited for phalanx warfare. The Romans apparently began to copy shields, sword, and missile attack from some of their opponents.
The main weakness of a phalanx system is that it is somewhat one dimensional in its purest form--a single extended line. It is also very vulnerable to anything disrupting it. The lack of depth is a substantial weakness. Most phalanx defeats resulted from some factor causing serious disruption of some portion of the phalanx. So if a portion of a phalanx is disrupted, it will likely be defeated, and the whole army might be routed with proper exploitation. Alexander and Hannibal used combined arms rather than relying on the phalanx alone. Cavalry dealt the decisive blows. By comparison, Rome did not field substantial cavalry.
Rome also relied on heavy deep infantry assault to break enemy lines. This fits with the aggressive nature of Roman warfare. The phalanx has a more defensive posture about it. And it is more difficult for hoplites to chase down defeated enemies. Pyrrhus could not complete the destruction of the Romans in either of his first two battles/victories against them. His phalangites could not conduct an effective pursuit.
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