The camera has a watch battery inside that has expired. Many of the Canon Powershots have external access doors for replacement of this battery. Unfortunately though for the A80 it's not easy to replace. It's buried deep inside the camera behind the card reader slot. It can be viewed on page 4 of the following disassembly of a very similar A95:
Due to the complexity of accessing the battery, do NOT recommend that you try replacement yourself. Instead recommend that you continue to bypass on startup.