Why does the drive fault to “3-phase fail” after the drive is enabled?

The three-phase voltage isn't present at the input of the drive.

• Verify the 3-phase voltage at terminal L1, L2, and L3 is at the rated amount with an Oscope at time of power up. If you're getting a spike or drop out that is quicker than a multimeter to see then you require an Oscope.
• Check all fuses (Including the coding fuses on the Power Board). The manual of the 590+ has a power board layout of the drive -- dependent on the frame size  -- that has a diagram of the fuses that run along the input terminals you should check.
• A common cause (that is application-dependent) is an Emergency Stop fitted into the system that has cut power to the input terminals. If you have an emergency stop on the system tied to the input mains, check that wiring and ensure it is not interfering or removing power.
• If there's input components (eg line reactors) then verify their connections and associated ratings

[QuickLink for the 590+ on Parker.com] - Manual, QuickStarts, Product Support, etc