New battery on a harley Davidson keeps dying?

To properly diagnose most electrical issues you will need a multimeter, which is a test tool that is used to test electrical current, load, and resistances. There can be several potential issues that can cause a battery to discharge. If the battery is discharching while the machine is sitting for a short period of time, there is some current draw in the machine that is using electricity; suspect a shorted out connection. However, if the battery is failing after being ridden, then the culprit could be the charging system. The procedures to correctly diagnose either of these problems, along with a host of others, can be found in your model year's Service Manual; for around fifty dollars, it is a very wise investment.