She often misses work under the pretext of being sick from her period.
She often skips work because she is not feeling well due to her period.
ーShe often misses work under the pretext of being sick from her period.
「彼女はしょっちゅう生理の体調不良を言い訳に仕事を休む」
under the pretext of ...「…を口実に・…にかこつけて」
pretex を使って言えますが、とても固い言い方になります。
ーShe often skips work because she is not feeling well due to her period.
「彼女はしょっちゅう生理の体調不良で仕事をサボる」
to skip work で「仕事をサボる」
このように言った方が自然な感じがします。
ご参考まで！
カナダ 
