Assuming the battery is not being recharged during the time the load is connected then the internal resistance value stays the same initially when the load is connected then increases in value as the present energy stored in the battery is being consumed by the load.
The internal resistance of a battery is at it's minimum value when the battery is fully charged. The battery's internal resistance approaches it's maximum value as the battery approaches full discharge.
Technically it increases..... Bcos as soon as current starts to flow temperature of a battery increases and hence the internal resistance, however its increment is so small that we can neglect it..... :)
Same
