That is the line I was thinking.
When the bike sits for several days and you turn on the ignition but do not try to start it, is the clock still right?
Does the clock then reset when you start it?
If the clock is right before you hit the starter, that means that the voltage is dropping way down while cranking.
This could be a battery issue, or a dirty connector issue, or something that is still drawing the battery down issue.
I am kind of leaning to an issue in the clock. On my 1st gen the battery can be low enough that it will not turn the bike over but it does not bother the clock.