It's like somebody dipped [Sips'] arm into acid … Sips tries to cast Sleep on himself to try to get away from the pain, but he fails his concentration check … Gothi quickly shoves a sleeping potion down Sips' throat to make him fall asleep but he succeeds his save, so his body won't take it and he won't fall asleep.
Can someone intentionally fail a saving throw in Dungeons & Dragons 5th edition?
According to Lead Designer Jeremy Crawford, ‘No rule lets you opt to fail a save’. In cases like these, the DM might discretionarily allow this under certain circumstances.
However, I disagree with Crawford on this interpretation of the rules ‘as written’. What follows are my reasons.
In 3.5e, the Player's Handbook contains an explicit rule about voluntarily failing spell saving throws:
Voluntarily Giving up a Saving Throw: A creature can voluntarily forego a saving throw and willingly accept a spell’s result. Even a character with a special resistance to magic (for example, an elf's resistance to sleep effects) can suppress this quality. (3.5e PHB 177)
In contrast, Crawford is right in the sense that the 5e Player's Handbook contains no such explicit rule.
However, the 5e Player's Handbook says of saving throws:
A saving throw—also called a save—represents an attempt to resist a spell, a trap, a poison, a disease, or a similar threat. (5e PHB 179; emphasis added)
The Oxford English Dictionary defines ‘attempt’ as ‘A putting forth of effort to accomplish what is uncertain or difficult; a trial, essay, endeavour; effort, enterprise, undertaking.’ It is clear from this definition that to ‘attempt’ something necessarily requires an affirmative ‘effort’.
Sometimes, this ‘effort’ is not a conscious decision. A Constitution saving throw to avoid contracting a disease, for example, represents a body's natural defences. A creature cannot voluntarily control their body's immune function, so it would appear difficult to justify allowing a creature to voluntarily fail such a saving throw. (On the other hand, a creature could attempt to subvert some of their body's normal defences by, for example, contacting more of an infectious source than usual. It could be appropriate to model these situations by, for example, rolling a saving throw with disadvantage.)
In other situations, however, this ‘effort’ may be a conscious decision. A creature who makes a Strength saving throw to avoid being bowled over may well do so voluntarily. So long as that character is sufficiently aware of the threat, the creature could just as easily choose to go limp and not resist. In these situations, where a creature chooses not to ‘attempt to resist’, it would follow that there can be no corresponding saving throw.
The 5th edition Player's Handbook also states that:
In cases where the outcome of an action is uncertain, the Dungeons & Dragons game relies on rolls of a 20-sided die, a d20, to determine success or failure. (5e PHB 7; emphasis added)
In the usual cases of a saving throw, the outcome is indeed uncertain: Who will win, the threat, or the creature attempting to avoid the threat? Conversely, in cases where the creature voluntarily relents to the threat, the outcome is a certainty – the threat will succeed. It therefore follows that no dice roll is called for.
The following rule has often been relied on to counter this argument:
You don't normally decide to make a saving throw; you are forced to make one because your character or monster is at risk of harm. (5e PHB 179)
It is argued that the use of the phrasing ‘you are forced to make one’ means that there can be no choice. I would not consider this to be the correct interpretation of this rule.
The Oxford English Dictionary here defines ‘force’ as ‘To compel, constrain, or oblige (a person, oneself, etc.) to do a thing (†sometimes with to omitted); to bring (things), to drive (a person, etc.) to or into (a course of action, a condition)’. The second part of this definition is of particular relevance: ‘to drive a person to a course of action’.
In general usage, to ‘force’ someone to do something does not necessarily literally mean that the person is physically incapable of choosing otherwise. To ‘force someone's hand’, for example, might mean only that a particular course of action is a person's best choice, despite there being other (albeit inferior) choices available to the player.
In my view, the rule above should more correctly be read:
You don't normally decide to make a saving throw; the circumstances are such that your character or monster will come to harm unless you make one.
This more forgiving reading of the word ‘force’ is consistent with the definition of ‘saving throw’ above being an ‘attempt’ requiring an affirmative ‘effort’. To adopt a stricter interpretation would create situations where a creature has their freedom taken from them and is inexplicably compelled by some insurmountable supernatural force to mount a conscious effort to resist against their will.
When interpreting documents like rules, there is a presumption against interpretations that would lead to unreasonable or absurd outcomes : See, for example, L Schuler A G v Wickman Machine Tool Sales Ltd  2 All ER 39. It is unreasonable to force a creature to stand their ground when they wish to relent, and so a strict interpretation is contraindicated.
Some saving throws are not based on conscious effort and cannot be voluntarily failed, but it may be appropriate for these to be rolled with disadvantage. Other saving throws are based on conscious effort, and a careful holistic reading of the rules supports the proposition that these saving throws can be voluntarily failed, despite the absence of an explicit rule to this effect.
At the end of the day, as always, it will be up to the DM's judgment and discretion whether to accept this reasoning, Jeremy Crawford's advice, or some other viewpoint entirely.