I have the same problem with my tangerine iBook.
I believe it is a battery problem, the battery can no longer hold a charge thus either will not work off of batter power alone, or messes with the date & time.
Please check on the upper-right of your screen, near where the date and time is located. Is there an icon of a battery with an "x" through it? This means you need a new battery.
They cost around $130 and can be purchased at CDW or Mac Mall, or a few other 3rd party Mac distributors.
edited to add:
From the CDW website:
"Even rechargeable batteries wear out. After repeated use and recharging, batteries simply lose their ability to store power. Under normal use, a Lithium ion battery can keep your notebook running longer on a single charge, but they may last an average of only 400 use and recharge cycles, or about a year of normal use. "
So if you have used your ibook 400 use/recharge cycles... then it may be time for a new one.