Problem when the battery is low and I plug in the power cord

[chiefpatrolman]

I will frequently run on my T60p battery, then when it gets down to 25% or so, plug in the power cord.

Lately, I have been having a strange problem when I do this: the "charging" icon does not appear, and the cursor freezes!

All I can do is turn the machine off and power up again, at which time the icon is present, normal charging occurs, and the cursor works.

Why does this happen, and what should/can I do to prevent it from happening?