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Some settings in the Symbology tab require that a histogram is built (e.g., using the Classified renderer, or using a histogram stretch). If a histogram is not present, ArcMap prompts the user to compute the histogram.
If a histogram is computed, that histogram is not persisted in the raster dataset; it is only persisted for that particular ArcMap session. The next time the same raster dataset is used in a new ArcMap session, the histogram must be computed again.
This is caused by a bug that affects the histograms for the IMG and TIFF formats in ArcGIS 9.3.
To persist the histogram in the raster dataset, calculate the statistics for that dataset using the Calculate Statistics geoprocessing tool.