Lithium-ion polymer batteries have such a problem.
"During discharge on load, the load has to be removed as soon as the voltage drops below approximately 3.0 V per cell (used in a series combination), or else the battery will subsequently
no longer accept a full charge and may experience problems holding voltage under load."
https://en.wikipedia.org/wiki/Lithiu...nd_limitations
it's something often discussed in the fourm, you might use search button to find more.