There's many a slip 'twixt the cup and the lip is a very old proverb, similar in meaning to "don't count your chickens before they hatch". It implies that even when a good outcome or conclusion seems certain, things can still go wrong.
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Origin
The English proverb is almost identical with a Greek hexameter verse, Πολλὰ μεταξὺ πέλει κύλικος καὶ χείλεος ἄκρου (Much there is between the cup and the tip of the lip). This verse was proverbial at the time of Aulus Gellius (2nd century A.D.), who mentions it in his comment on the Latin phrase inter os atque offam (between the mouth and the morsel) used by Marcus Cato. The Greek verse is attributed to Palladas in The Greek Anthology (X, 32), but that is manifestly erroneous, since Palladas lived two centuries after Aulus Gellius. The Loeb Classical Library edition of the Anthology says that the verse is "a very ancient proverb, by some attributed to Homer". There is a reference to the many things that can intervene between cup and lip already in an iambic verse by Lycophron (3rd century B.C.) quoted by Erasmus.
According to a story about the proverb, the verse was a comment by a seer who told Ancaeus, who was setting out on the perilous enterprise of the Argonauts, that he would never taste wine from his newly planted vineyard. On his safe return, Ancaeus filled a cup with the first wine from his vineyard and reproached the seer for what appeared to be a false prophecy. The seer responded with the verse and just then an alarm was raised that a wild boar was destroying the vineyard. Without tasting the wine, Ancaeus rushed out and was killed by the boar.
The proverb may have been inspired by a situation described, without the proverbial phrase, in Homer's Odyssey, Book xxii 8-18 (from c. 850 B.C.), where Odysseus kills Antinous, who "was on the point of raising to his lips a fair goblet, a two-eared cup of gold, and was even now handling it, that he might drink of the wine, and death was not in his thoughts".
Usage
As mentioned above, Aulus Gellius considered the phrase inter os atque offam to be a Latin equivalent of the Greek proverb. Other equivalents or citations have been discerned in one of Cicero's Ad Atticum letters in 51 B.C. and in the anonymous 13th-century French work De l'oue au chapelain, There is a slight similarity between the wording of the proverb and that of an unattributed Greek iambic trimeter verse quoted by Cicero in a letter to Atticus, but this refers to the geographical distance between Cicero and his correspondent.
Erasmus's 1523 Adagia, in which he translated the Greek verse proverb into Latin verse as Multa cadunt inter calicem supremaque labra was the basis of translations into many languages. An English translation by Taverner in 1539 rendered the proverb as "Many thynges fall betwene the cuppe and the mouth ... Betwene the cuppe and the lyppes maye come many casualties".
The proverb appears in English also in William Lambarde's A Perambulation of Kent in 1576: "[M]any things happen (according to the proverbe) betweene the Cup and the Lippe". In the same year, George Pettie added to it: "Many things (as the saying is) happens betweene the cup and the lip, many thinges chaunce betweene the bourde and the bed" in Petite Palace. The version "manye thinges fall betweene the cup and the lippe" appears in 1580 in John Lyly's Euphues and His England. In Ben Jonson's play, A Tale of a Tub (1633) Erasmus's text is explicitly quoted and expanded: "Multa cadunt inter—you can ghesse the rest. /Many things fall betweene the cup, and lip: /And though they touch, you are not sure to drinke."
Literary
While a group of banditti ransack Mrs. Archer's house, the leader, Sam Hewson, drops a bottle of brandy; after it shatters, he says, "Ah, my men! there's a sign for us – we may have a worse slip than that 'tween the cup and the lip: so let's be off – come, Pat."
Later in the novel, the narrator recounts, "That 'there is many a slip between the cup and the lip' is a proverb somewhat musty; but it pithily indicates the sudden mutations to which poor humanity is liable."