A large percentage of mortars used for masonry construction projects contain some pigments. I read that retempering should not be permitted with these products.

Is it true? If so, what can be done when the mortar starts to stiffen?

Retempering can alter the color of the mortar, which in some cases creates a blotchy appearance. Most suppliers of mortar pigments or pre-bagged pigmented mortars do not recommend retempering.

Mortars that are not retempered must be discarded as soon as they begin to stiffen. On many projects, this situation would necessitate mixing small quantities of the mortar that is used up quickly. However, the variations are small with most colored pigmented mortars.

It is generally better to have some color variations than to complete masonry walls containing multiple separations or poor bond between the mortar and the masonry units because the mortar was too stiff when used. Significant variations are more likely to occur with some dark colors and with mortars that contain significant quantities of pigments.