It was irritating when the emergency alarm kept going off in the middle of the night.
「住んでいるアパートの非常ベルが誤作動で頻繁に鳴ります。」は英語で「The emergency alarm in my apartment goes off frequently due to a malfunction.」という表現が良いと思います。
「昼間ならともかく深夜に鳴り続けると本当に迷惑。」には英語で「It's not so bad when it's during the day, but it's really annoying when it keeps on ringing late at night.」です。
Alarm goes offーアラームが鳴る
アメリカ合衆国 
