I would guess you're thinking about the phenomenon called creep.
Your piece of metal is made up from crystals in which each atom has a well defined position with respect to the atoms around it, and it takes a lot of energy to make an atom jump completely out of its position. When you elastically deform the metal you displace atoms very slightly, but when you release the metal the atoms return to their equilibrium positions and the metal returns to its original shape. Permanent deformation happens when you apply so much force that it makes some of the atoms jump completely out of their original locations and into new positions.
However even under small deformations it is possible for atoms to move causing the deformation to become permanent. Metals generally contain defects in their crystal structure called dislocations and the atoms near a dislocation are generally more mobile than atoms in the rest of the metal. Under even small applied forces movement of atoms at a dislocation can cause the dislocation to move and the metal to permanently deform.
Alternatively, at any temperature above absolute zero the atoms in a metal have some thermal energy so they are vibrating about their equilibrium positions. As you increase the temperature the atoms vibrate more and this makes it easier for them to move. The obvious extreme example of this is melting, where the atoms vibrate so much it breaks down the regular crystal lattice and becomes a liquid. However even below the melting point increased temperature can allow atoms to move and this can cause a small deformation to become permanent.
To what extent creep happens, and how fast, depends on the type of metal and how the metal has been treated. Obviously your tweezers are designed to be flexible and will have been made from a metal that does not creep readily.