According to the Wikipedia page on portrait painting in the middle ages, it was not until after 1350 that portraits ‘became clear likenesses’.
This seems to be confirmed, for England at least, by the following text on Richard II
This wooden panel-painting is the earliest known portrait of an English monarch, dating from the 1390s.
In France, it seems that Charles VI (died 1422) was the first monarch there to have his likeness captured by a contemporary artist, in 1412. It also appears that the large majority of portraits of pre-1400 monarchs such as Henry II of England and Louis VII of France were done during the 17th and 18th centuries.
This is puzzling given that accurate portraiture was common enough in ancient Greece and continued up to the 4th century in Rome (at least). After this,
the interest in an individual likeness declined considerably.
What were the reasons for this decline and why did it take so long (much longer than the Dark Ages lasted) for Europeans to become interested in lifelike portraits?
Judging by the exquisite artwork found on early medieval manuscripts, the reason could not have been lack of talent. Granted, this is a different kind of art but there is no reason, I think, why skilled portrait artists could not have flourished had there been a demand for them.
Also, for people (crusaders for example) who were away from their homeland for a long period of time:
Wouldn’t people with sufficient means have wanted and been able to afford visual images of family members and loved ones?