For Delta-E values of less than 2 there is almost certainly no need to recalibrate. For values higher than 3 it is important to understand what the cause is, and if it is significant.
The calibration and adjustment process has inherent variability due to many factors such as the repeatability of color sensor measurements, and changes within the display as it is adjusted. The basic accuracy and repeatability specifications for most sensors is typically +/- 0.002 or higher for CIE xy, and +/- 2% for luminance. These variances alone can give rise to Delta-E values of up to 2 or 3.
When a specific Intensity value is being used for the calibration, the Delta-E value is comprised of the luminance and color differences. Differences in color are much more critical than a difference in relative luminance. Look at the results of the calibration shown in the Information window to determine if the high Delta-E value is caused mainly by a shift in color or in luminance.
High Delta-E values can also occur if a specific Intensity value is being used for the calibration and the display is not capable of achieving the specified Intensity value. The calibration will always aim to achieve the specified White Point, even if the Intensity value could not be reached. If the display can not be calibrated to achieve the specified Intensity value modify the value accordingly.
In some situations, the display Intensity will drift slightly for several minutes after it is adjusted. Since the measured value used to calculate the final Delta-E result is taken up to one or two minutes after the display was adjusted, a higher Delta-E value may be shown, even though the calibration process achieved the specified Target values during the calibration process. Selecting the Extended luminance stabilization time option in the Preferences can be used to try and minimize this effect.