My PCs are currently playing through Rise of Tiamat and in a session or two will be fighting an adult white dragon.

Arauthator, the boss monster of Episode 2

Because they are currently at a higher level then their episode is set for, I expect that they will win the set-piece confrontation in the dragon's lair, and he will retreat.

The module specifies that "Maccath knows that surprise is the characters’ best weapon for challenging the dragon, and that he will not risk dying over this single lair. Though he hates the idea of abandoning a home with its treasure and trophies, if bested by the adventurers, Arauthator will flee to one of his other lairs...When the dragon is reduced to 100 hit points or fewer and facing three or more foes, he dives for this exit and escapes into the frozen sea."

However, the module assumes that once the dragon flees, he ceases to be an antagonist. As DM, I have decided that he will instead heal up and then at least consider harassing the party for a while, especially if they have made off with some of his treasure.

In particular, one cold breath could easily clear the Frostskimmr's deck of normal sailors, potentially becalming the party, none of whom have a sailing background, and allowing him to continue to strike at them over the many days it might take them to leave the Sea of Ice.

The party in part consists of a paladin, who is only effective in melee, an armorer artificer, who mostly melees with thunder gauntlets but who has a few ranged spells, and a commanded shield guardian, who also is only in melee. The ranged attacks of the party are principally those of their arcane trickster and evoker. Thus, even though the dragon will be absent his lair actions, he may actually fare better against the party in the open than in his space-constricted lair. I intend him to employ a strategy of strafing the party at the maximum distance with his cold breath, then retreating / dodging until it recharges, and repeating.

The dragon does not yet know that the party has access to both Water Walk and Water Breathing. He will likely open with an attack from below which attempts to upset the ship and dump as many people into the water as possible as per the Merrow encounter, and he will certainly use the water as cover during the fight.

However, the dragon is much more interested in surviving than in revenge. If the party demonstrates (either in the initial battle or the possible later one) that they have the ability to take him out despite his hit-and-run tactics, he will give up pursuit of them. And the 60' range on his cold breath is rather close for comfort; there are a lot of things even a melee-heavy party can do at 60' at 10th level.

So, what are things that the dragon would consider deal-breakers? That is, what sorts of things would he have to observe from the party to conclude that he is better off letting them go?

For example, a failed save against an incapacitation spell could lock him in place and allow the party to enter melee, where he has already been beaten. His Legendary Resistance will help with this, but if he learns that the party has multiple casters capable of such spells, he would not put himself in a position where he could be targeted by any number of such spells in one round that is more than the number of uses of Legendary Resistance he has remaining.

What are other, similar, rules of thumb he should use in order to determine when he is dangerously over his head? What specific abilities would he recognize as having the potential to incapacitate or kill him before he could respond by fleeing?

Assume that he does not know what spells the party has until they use them, but that he can recognize the spells and knows their complete descriptions including range. Assume that he can recognize their character classes after they use class-specific abilities and then knows what other class abilities they have.

Relevant information: Shield Guardian

Paladin (Oath of Vengeance / Dueling) - Stone of Good Luck, Crusader Shortsword, Greatsword +2

Rogue (Arcane Trickster): Magic Items - Cloak of Protection. Spells: Message, Mage Hand, Prestidigitation, Sapping Sting, Minor Illusion, Silent Image, Disguise Self, Find Familiar, Shield, Mirror Image, Shadow Blade, Tasha's Mind Whip

Artificer (Armorer)
Infusions - Cloak of Protection, Homunculus, Helm of Alertness, Strength Armor, Enhanced Weapon, Enhanced Defense Spells - Mending, Firebolt, Shocking Grasp

Wizard (Evoker) Magic Items - Amulet of Shield Guardian Command. Spells - Minor Illusion, Firebolt, Prestidigitation, Chill Touch, Shocking Grasp, Acid Splash. Detect Magic, Sleep, Mage Armor, Unseen Servant, Witch Bolt, Identify, Magic Missile, Thunderwave, Chromatic Orb, Shield. Darkvision, Knock, Misty Step, Rope Trick, Cloud of Daggers, Mirror Image, Acid Arrow. Fireball, Fly, Haste, Counterspell, Tiny Hut, Sending. Black Tentacles, Wall of Fire, Greater Invisibility, Ice Storm. Cone of Cold, Arcane Hand, Synaptic Static.

Related: How should I set up and execute air battles in my session to avoid easy encounters?

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    \$\begingroup\$ Before there can be a good answer for "what" there needs to be a strong "why". Why would a dragon that has fled to escape destruction by a superior force choose to attack again? Revenge is a good motive, but unless certain of success, why should a dragon risk both personal destruction and getting a rep for being repeatedly beaten and running away? More importantly, why do you as a GM want to add a follow-up encounter to a party that is already above the intended level? Are you trying to teach them to always kill enemies and never allow any that flee to escape? \$\endgroup\$ Jun 21, 2021 at 7:01
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    \$\begingroup\$ Dragons think in timelines different from humans. Decades. Why doesn't the dragon just sit it out and kill them when they are old? \$\endgroup\$
    – Trish
    Jun 21, 2021 at 8:33
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    \$\begingroup\$ I doubt there would be an absolute answer based on how many parameters there are to look at to answer, thus becoming very broad. While it is a very interesting question, I think it'll generate too many opinion-based answers, so I'm voting to close it. \$\endgroup\$
    – Zoma
    Jun 21, 2021 at 8:34
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    \$\begingroup\$ @Trish First, the canon description of white dragons. "They are vicious, cruel reptiles driven by hunger and greed...[they are] singularly focused on surviving and slaughtering their enemies...They recall every slight and defeat, and have been known to conduct malicious vendettas against creatures that have offended them...White dragons are notoriously difficult to bribe, since any offers of treasure are seen as an insult to their ability to simply slay the creature making the offer and seize the treasure on their own." \$\endgroup\$
    – Kirt
    Jun 21, 2021 at 15:41
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    \$\begingroup\$ I think this is stackable now. \$\endgroup\$
    – Akixkisu
    Jun 21, 2021 at 16:34