No universo, ela era a chefe da Starfleet Medical.

De "A criança":

WESLEY: It's going to be hard leaving the Enterprise.

PICARD: Mixed feelings for all of us. It's always difficult leaving any ship, just as it was for your mother when she left to become head of Starfleet Medical.

Quando ela voltou, não muito foi dito, mas em "Evolução" está implícito que ela pode ter retornado porque era difícil ser separado de Wesley:

PICARD: If you're concerned about Wesley, I see no evidence that there's a problem.

BEVERLY: I know. In a funny kind of way...that's exactly my point. We talk. We smile. It's almost too polite.

PICARD: Beverly, this is simply a matter of time. I know how difficult it was to be away.

BEVERLY (vulnerable): Tell me about him.

O escritor Maurice Hurley, fora de universo, na época, não gostou dela.

Gates McFadden fired at end of first season because head writer Maurice Hurley "he had a real bone to pick" with Gates and din’t [sic] like her acting, Berman brought Gates back for 3rd season after Hurley left

(Essa citação é do resumo aqui .)

Este comentário também cita o cabelo dela (de todas as coisas) como custando muito tempo e dinheiro para manter o estilo certo para evitar problemas de continuidade. Não tenho certeza se compro, mas aí está.

De acordo com a Memória Alfa , Crusher foi cancelado devido às dificuldades que os escritores estavam tendo. com ela:

Officially, the difficulties in developing Crusher's character led to her character's departure by the second season. Unlike Natasha Yar, however, the TNG writing staff reassigned Crusher to Starfleet Medical, leaving open the possibility for her return. The writing staff's dissatisfaction with the Pulaski character, fan pressure via a letter-writing campaign, and support from Patrick Stewart allowed this to happen during the third season.

Esta citação também diz que a equipe não gostava de Pulaski, e tanto os fãs quanto Patrick Stewart queriam que Crusher voltasse ao programa.

Ela foi demitida

De acordo com sua página na Memória Alfa , ela queria seguir outras direções nela carreira.

De acordo com a Memória Alfa:

McFadden left the series at the end of the first season and was replaced by Diana Muldaur as Doctor Katherine Pulaski in the second season. An official announcement states, that McFadden had left the series to pursue other career options. McFadden herself got a call from her agent who told her that the producers decided to go in another direction with the character. Like the other cast members, McFadden was surprised. ("Gates McFadden - Dr. Beverly Crusher", The Official Star Trek: The Next Generation Magazine Vol. 12, p. 43)

Curiosamente, não é isso que Wikipedia tem a dizer:

At the end of the first season, McFadden was fired and replaced by actress Diana Muldaur as the Enterprise's Chief Medical Officer.

Este trecho faz referência à seção seguinte de uma entrevista com o diretor Rick Berman:

Gates McFadden fired at end of first season because head writer Maurice Hurley "he had a real bone to pick" with Gates and din’t like her acting, Berman brought Gates back for 3rd season after Hurley left

( Source )

Quanto ao retorno dela:

But thanks to a letter-writing campaign, support from Patrick Stewart, and a personal invitation from Rick Berman, McFadden was brought back to the TNG cast for the third and subsequent seasons. McFadden was absent for all episodes of the second season and only appeared in stock footage in "Shades of Gray" which was used from the first season episodes "Symbiosis" and "Skin of Evil".

Aparentemente, houve desapontamento por Hurley não corresponder às expectativas:

Muldaur's character, Dr. Katherine Pulaski, didn't make it to the third season. Roddenberry described Muldaur as "a most talented actress", and said that the decision "to let her go was made solely because the hoped-for chemistry between her and the rest of the starship cast did not develop."

( Fonte )

E, apenas para esclarecer a razão do universo , foi oferecido a Crusher uma posição como a cabeça da Starfleet Medical de acordo com Memory Alpha .

O que eu lembro daquela época, mas ela foi cancelada porque simplesmente não conseguia agir. Ela entrou com uma queixa sindical, e basicamente teve sorte que os fãs odiavam Pulaski e eles precisavam de uma solução. Todo o resto do roteiro "sexista" era um absurdo. Até hoje, a maior parte do elenco ainda não a apóia.