Repairing units yourself (including battery replacement) will probably void any warranty, so don't do this unless you are happy to risk that.
Having said that, the battery, beeper components and o-rings are available for a few dollars each, so if you are a long way from the nearest authorised SPORTident repair-man, you may want to try this.
See the guide on the Big Foot site for detailed instructions. See the guide on the sportident.us web-site. You will need to be able to wield a soldering iron with at least a little confidence.