Related Clues:

• A hairline may do it
• Under-mine
• Vanish over time
• Decrease, as support
• Eat away at the bank?
• Wear in bad weather?
• Develop ruts, say
• Destroy steadily
• Slowly disappear
• Gradually destroy
• Siphon off, as support
• Deteriorate slowly
• Undermine, as confidence
• Reduce bit by bit
• Wear away, as a beach