It's a XD8500 cordless phone.
On one of the Handsets the LED display goes dull, then disappears only to return later.
Is there any way of correcting this?
Yes, & the battery indicator on phone shows full charge.
Possible a faulty display, is it LED or LCD? LCD displays often show this problem, but it unusual for LED displays.
Some LCD phones have a backlight, and that can give problems. Some also have a standby mode where the display is dimmed to save power.