Much is going to depend upon the quality of the dyes and textiles in question. Then will come how one cares for item.
Strictly speaking laundering in water will cause some loss of excess dye. This is normal the first several washings or so, but afterwards more damage comes from how and what one uses to launder items than anything else.
Bluing agents, optical brightening chemicals, bleaches, high water temperatures and so forth can and will cause certain colours to fade. Contrary to popular myth there is no such thing as "colour safe" bleaching, and that includes oxygen based. If something will remove color than sooner or later with repeated use it will affect dyed textiles, especially darker shades.
The chlorine bleach in tap water depending upon amounts will eventually work upon dyes as well.
Happily modern detergents especially those designed for colours contain a wealth of chemicals such as polymers to help preserve dyes and mitigate loss.
Harsh caustics such as washing soda can affect colors over time as well.
You also want a product that rinses clean without leaving residues. This is one reason so many like liquids for colored items over powders. Especially for darker colors you want to avoid powders containing things like Zeolites which are insolable.
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