No, I misspoke. A battery can only be discharged, then plugged in and recharged, a finite number of times, depending on the chemistry of the battery (L-ION v. Nickel Metal Hydride etc.).
If it's always plugged in, or even almost always plugged in, there should be no problem. It's hard to tell what's going on without more info, like a model number for instance.
When I get home, I'll look and see. It's a bit annoying though.