CellLabelAutoDelete is an option for Cell which specifies whether a label for the cell should be automatically deleted if the contents of the cell are modified or the notebook containing the cell is saved in a file.
Cells that represent Mathematica input and output typically have CellLabelAutoDelete->False.
CellLabelAutoDelete is more often set for styles of cells than for individual cells.
See The Mathematica Book: Section 2.10.9.
See also: CellLabel, ShowCellLabel, CellTags, CellAutoOverwrite.