Help - Rows being sent to the bottom of sheet (disappearing) and can't figure out why

Our scheduling sheet has about 50 lines on it per day, and each new day we copy and past the previous workday to make the new schedule. So at the moment, the sheet reaches back about 3700 lines to July 1st.

Sometimes (including today, just now) lines being used for the current day will get automatically shifted to the bottom of the sheet (line 3709) and it effectively disapepars from the current day's schedule, causing mass panic and confusion to everyone who notices.

How do we fix this?