Possible Clues:

• Peter out with tough conservative
• Bruce Willis flick
• One who just won't give up
• Did hear model is set in her ways
• 1988 movie set in the Nakatomi Plaza building
• Ultra-conservative
• Reactionary has special hide-away
• Stubborn fellow? I'd heard otherwise
• Hire dad (anag) — one who sticks to traditional views
• 1988 film starring Bruce Willis (3,4) — one strongly opposing change