Hi Les,
If you had a low battery but were able to start the bike then you let it idle for 15 minutes and then you could not re-start it that says to me very flat battery.
As I have said to another member recently when a K is idling it is not charging the battery it is running it down more every second it idles. If you start the bike and then ride off and give the bike a good run for say an hour or so at reasonable highway speed, not idling in traffic, that will recharge the battery. After you switch off then it will re-start. That is a typical sequence for a bike with no other problem other than a battery in a low state of charge.
Regards,
K-BIKE