Deleting rows w/out losing references

I have a sheet of data that I'm trying to delete a row from. When I delete the row, all the rows below it change to #REF, and I guess I lose all the references to my formulas. I had a similar sheet of data that I could delete rows from without this happening, so I know it can be done, but how?
Let me know if any further info is needed to help solve this problem.
Thank you.