Why would a new battery go flat within 3 days on a jag xjr?

Three reasons come immediately to mind: First, it was a bad (shorted) battery and it simply went. Second, the charging system is not operating properly. When the new battery was installed, that should have been thoroughly checked, because anytime a battery dies, the cause has to be determined in order to prevent a recurrence. If it wasn't checked, it should be now to be sure it's not, for example, the alternator that's not functioning properly. Third, from my own experience, my XJ had a defective computer running the security system, remote door unlock devices, etc. and it burned a few batteries before it finally burned out the seat memory controls and then they were able to identify it as the cause. They were right, it turned out.