It is normal functionality in Excel, that clipboard is emptied when you delete a value from cell.
I have two suggestions:
1) Just Paste. Don't clear the area first. If you have entered formulas to area, you will be asked, whether you want to replace those or not.
2) If you need to delete cells for some reason first, with Excel 2003 you have also Office Cliboard to use:
- open Task Pane (View | Task Pane)
- on top row of Task Pane there is a "dropdown arrow" to open a menu, where you can select Clipboard
- on that Clipboard view you can see 24 last copied objects; select the one you need to paste and just paste it.
Please, ask me further instructions, if needed.