The doctrine of Separation of Powers divides government responsibilities into three branches — Executive, Legislature, and Judiciary — to prevent abuse of power and ensure checks and balances. When discussing challenges faced by the judiciary under this doctrine, the focus is on issues that affect judicial independence and balance of power.
Judges are often appointed by the executive (e.g. President or Governor), which can compromise judicial independence if the process lacks transparency. If the judiciary does not control its own finances but depends on the executive for funding, it undermines its independence. When the executive or legislature has excessive influence over how judges are removed, it threatens judicial independence.
But, while poor legal infrastructure is a real challenge for the judiciary, it is not directly related to the doctrine of separation of powers. It is more of a logistical or administrative issue.