毎日 and 連日: each day and a run of consecutive days
Compare a daily reading habit with an event running over consecutive days, including a future schedule using 連日.
Each day within the relevant range
毎日, read まいにち, means every day. 毎日、寝る前に本を読みます。 describes a habit of reading before bed each day.
今週は毎日図書館に行きました。 says that the person went to the library every day this week. 今週 supplies the range of days being discussed.
Several days in succession
連日, read れんじつ, refers to consecutive days. 連日、多くの人が展示を訪れました。 says that many people visited the exhibition on consecutive days.
来週は連日公演が行われます。 says that performances will take place on consecutive days next week. 連日 can also describe a future schedule.
Overlapping meanings and a bounded run
Both 開催期間中は毎日開きます。 and 開催期間中は連日開きます。 can describe opening each day during an event. 連日 emphasizes the succession of days.
連日開いています。 does not establish that opening will continue forever without a day off. Check the event period or operating schedule to identify the relevant days.
Does 来週は連日公演が行われます。 report performances that have already finished?
Show the answer and why
No. It schedules performances on consecutive days next week. 連日 itself does not mark past completion.