As @Martin has commented, ArcMap locks source files so they that they cannot be changed externally so your workflow of joining Excel spreadsheets to shapefiles will make them uneditable while ArcMap has that table open. You could remove the join and remove the table, perform the edits and then add the table and join back, without quitting ArcMap. However, that would usually be slower to do.
Consequently, I think the workaround suggested by @AnserGIS of using a Personal Geodatabase feature class, instead of a shapefile, thus allowing you to directly edit in MS Access (with some risk) or ArcGIS for Desktop, and then linking your Access table and Excel spreadsheet may be worth you investigating.