From what I can understand there are a few reasons why the name may have been associated with a maid. All wives would have been maids to their husbands in biblical times and a gentlewoman in the Elizabethan era would have been a confidante and strong willed friend of the lady of the household, keeping her suitors at bay, requiring wit and diplomacy to maintain her position.
The name's first association with a maid was originally due to the biblical Abigail's lack of conceit in talking to her servants and her belief in what they told her. Abigail/ Abigayil learned that her wealthy husband Nabal was deceitful, disassociated herself from his rudeness and had faith that David, an outlaw at the time, would rise to be King David. By being on good terms with the masses, the servants, she was able to gather enough provisions to provide David and his followers with strength.
Said to have one of the longest female speeches in the Bible, she implemented a change to the fortune of the Israelites and through her powers of diplomacy and persuasion led David to reverse his oath of revenge. Known for her wisdom and intelligence, it is said that ?When Abigail saw David, she fell at his feet, and said ?hear the words of thine handmaid?" Persuasion was not going to be an easy task without some flattery.
David tells her "May you be blessed for your good judgment and for keeping me from bloodshed this day and from avenging myself with my own hands? If you had not come quickly to meet me, not one male belonging to Nabal would have been left alive by daybreak." Had she not been on good terms with her servants she would not have won David, nor possibly could she have left Nabal. You wouldn't know that I attended a catholic primary school, would you.
In Beaumont & Fletcher's 'A Scornful Lady' (1616), Abigail or 'Abigal - a waiting gentlewoman' as she is described in the cast list, is used as a term for a maid as a consquence of the biblical reference. She's first introduced as 'Mistres - Younglove' and continues to have a considerable and feisty role in the comedy asserting herself against various men. The name Andrew was, apparently, the equivalent for male servants at the time. Bible obsessed, the Puritans.
Lastly, a reversal of fortune and an aristocratic connection may have made the name popular as among differnt classes. In 1670, a relation of the Churchill family was given the name Abigail. Her London merchant father, lost out on a specultive deal early in her life, putting the family reputation at stake.
Baroness Abigail Masham, as she was later known, was born a cousin of Sarah Churchill, later Duchess of Marlborough. Lady Churchill, as she was known before being a duchess, was herself Lady of the Bedchamber to Princess Anne and invited her cousin within her own household, possibly to shield the family's reputation. By 1704, she was a close confidante of Queen Anne.
Personalities clashed as Queen Anne was said to favour Abigail over Sarah Churchill, made evident by her attendance of her marriage to Samuel Masham. Sarah Churchill was a Whig and Queen Anne was a Tory making the situation strained and now political. The queen instructed Marlborough to give command to Colonel Hill (Abigail's brother) and the Whigs were overlooked to give way to Abigail's cousin, Robert Harley, Earl of Oxford. She died as Lady Masham in 1734 having yielded considerable influence upon the Queen.
Some sources say that it may also mean 'fountain of joy'. My history tutor had this name and I've always liked it.