An Anvil of Doom is a tremendously heavy object, rarely moved from within its keeper’s forge. When properly set atop a perfectly level dais of stone blocks, it is not easily moved.
Once an Anvil of Doom has been placed on the battlefield during deployment it cannot be moved by its crew during the Remaining Moves sub-phase.
Note that an Anvil of Doom can still pivot freely at any time during its turn (the better to face the enemy) and may make a follow up move as normal.