Possible Clues:

• Sissy has swim round river
• Repeated word in a Chumbawumba title
• Liquid falling in small golbules, or a dull person
• Fall as from leaky tap
• Faucet noise
• Icicle, originally
• Finally shed tear, let drops fall
• Weakling died -- may he be at peace
• Sad type died, with appropriate prayer
• Icicles do it