Excel 2003

We use an excel spreadsheet to organize our production schedule. The file
is shared and can be edited by anyone. Orders are entered by TJ when
received and deleted when shipped. He then saves and closes the file. I
tend to leave the file open all day and periodically update the status,
saving after I do.

This morning TJ reopened the file some time after deleting shipped orders.
There were three rows missing scattered throughout the spreadsheet. Two
other rows had been duplicated. This is not an isolated incident. It has
happened multiple times a week.

The risk of losing an order is unacceptable. This used to happen maybe a
couple of times per month. Now, after sharing the file, it is much worse.

Is there any way to stop this? Are we doing something wrong?