Does it give any error messages? Can you create new hyperlinks in the file, and then save the file without getting a warning?
If you can work with hyperlinks on other files, then one possible cause, especially if multiple people have access to it, is that it was saved in the 95 format, which does not support hyperlinks (though they will still be blue and underlined). Try going to File->Save As, selec the "Excel Workbook" file type (something without 95 in the title), give it a new name, save it, close and reopen it, can you now insert hyperlinks and edit them? If so, then the original ones were stripped when it was saved as a 95 file.