。
She kept writing in her diary until she died.
Literal
She [topic-は] death [until-まで] diary [object-を] write-continued.
書きつづける is a compound verb: 書く ('write') + つづける ('continue'). The ~つづける suffix is highly productive — attached to a verb stem, it expresses 'keep doing X.' Examples: 走り続ける ('keep running'), 待ち続ける ('keep waiting'). まで marks a temporal endpoint here ('until X happens'); 死ぬまで literally 'until [she] dies.' The image of someone keeping a diary right up to death has a quiet dignity — the diary as life's witness.