Laptop doesn't detect when battery is charged

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I've had my laptop (Acer Aspire 3613) for a couple of months.  Since
yesterday, when I have the AC cord plugged in, it doesn't stop charging
when the battery is full.  (When I say 'full', it shows 99%, which is
normal, and obtaining a reading from the acpi bus shows that the charge
is not increasing).

Would this be a problem with the battery needing replacement or a
problem with the charging circuitry in my laptop? More importantly, is
my laptop likely to be damaged by leaving the AC cord in when this is

I tend to use my computer for long periods of time (up to twelve hours
sometimes) on AC with the battery in place, which I read can fry a
battery fairly quickly.  Is it a good idea to take the battery out when
using mains power?

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