As a battery ages, it loses its ability to recharge back to its
original capacity. How does this change the terminal voltage vs
discharge time curve of an SLA battery?
At any given discharge current the voltage will drop below cutoff earlier. The shape of the curve will in general be similar, but may be modified by how the battery has aged.
Since the capacity of a battery decreases with time, the discharge
rate for any of the given periods (for example C20) will also
decrease; this is because less capacity means less total charge and
therefore a smaller rate of discharge for a given period.
This is true, but not useful. A battery will always last the same time when discharged at a proportion of its actual capacity, by definition.
But the actual capacity of the battery is unknown until fully discharged, so it will be tested at a discharge current which is a proportion of the rated capacity. Discharge current is not reduced just because the battery may have aged.
And the cutoff voltage will increase due to the decrease in discharge
rate (for any given period) hence the curve will shift upwards with
No, the cutoff voltage is not raised just because the battery may have reduced capacity. The battery is rated to maintain voltage above a cutoff voltage that varies depending on discharge rate according to the values specified in the datasheet. As the battery ages its capacity, as measured against those cutoff voltages, reduces. When measured capacity drops below 80% the battery is considered to be 'worn out' - even if it could deliver higher capacity at lower current.
A common example of this is when the battery suffers from sulfation, which increases resistance causing voltage to drop more at high current, reducing the realizable capacity at rated discharge current. However at lower current, where the the high internal resistance doesn't drop so much voltage, the realizable capacity may be higher. Of course if it needs to supply high current for a certain application this higher capacity at low current is not useful.