The hard hat is a members only helmet used in the Tower of Life quest to gain access to the tower. Additionally, it enhances the Beckonemote when worn. To re-obtain if lost, the player can either talk to the workers or search the crates in the Tower. It can be stored in the player's costume room along with the rest of the builder's outfit.
You can also talk to 'Black-eye' and answer a few questions to obtain another one if lost. The answers are as following:
How many nails does it take to make a rocking chair? -- Three
What takes 3 planks, 3 cloth and 3 nails to make, and help remove light from a room? -- Torn curtains
I like fish and I want to put some in my garden, but I need a special water feature. What materials would I require? - 10 clay pieces