This does not refer to any issue with a battery but relates to Valve Regulated Lead-Acid units (often called Sealed Lead Acid batteries).
In a traditional lead acid battery acid is held in a liquid form which can be poured out or topped up. Sealed Lead Acid batteries hold the acid either in a glass mat (Absorbent Glass Mat Batteries) or mixed with a silicon to create a gel (Gel Batteries).
Both of these techniques radically reduce the amount of acid required by the battery to function and hence the term ‘Acid Starved’.
For more on lead acid batteries see What is a lead acid battery.