She has been in and out of the hospital.

Literal

She [topic-は] hospital-admission-and-discharge [object-を] is-repeating.

入退院 is a 漢語 compound: 入院 ('admission, going into hospital') + 退院 ('discharge') — both mashed together as 入退院 to mean 'going in and out of hospital.' Combined with 繰り返す ('repeat') and ~ている, it describes a chronic pattern.