Repulse

I play Alpha Strike targeting my Master Yi, Unstoppable and splitting 12 damage among three of the four enemy units at battlefields. If my opponent plays Flash in reaction to my Alpha Strike, moving two of the targeted units to base, can they then play Repulse and counter my Alpha Strike?

No, they cannot play Repulse targeting your Alpha Strike. (Except if both of the other chosen units have changed to a non-board zone, such as via the effect of something like Grim Apothecary's play effect, Heedless Resurrection's additional cost, or the instructions of Thrill of the Hunt.)

A spell that targets a game object creates a targeting relationship between it and the targeted game object. As long as that targeted game object remains on the board, that relationship is maintained even if the target no longer fulfills the targeting restrictions of the spell. Even if the units in this example aren't at a battlefield anymore, they are still being chosen by Alpha Strike. We know this is true because the spell remembers that it is targeting those units if they happen to fulfill its targeting restrictions again per rule 359.3.e.3. The only exception to this principle is if the units change to a non-board zone-in such a case, they are no longer the same game object and any relationship between them and the spell that targets them is severed. Even if they returned to the same battlefield, they won't be legal targets and the spell won't be choosing them.

359.3.e.3.If a target ceases to meet the targeting requirements while the spell is on the chain, then meets them again, it's a legal target.

It can help to visualize Alpha Strike's targets with a colored arrow pointing from Alpha Strike to those units. Even if the units move to base and are no longer legal targets, they are still being chosen by Alpha Strike; we can imagine that the arrow is greyed out, but still present. Meanwhile, if they moved to a non-board zone the arrow would disappear entirely, since the game object it is connected to no longer exists. Repulse cares about the number of those arrows that point to friendly units, not the color of the arrows.

359.3.e.9.a. If another spell or ability attempts to reference the number of game objects, players, or zones that a Finalized Chain Item targets, it will include any mistargeted choices, but not any targets that have changed to a non-board zone. Example: When a player moves their Volibear, Furious to an occupied enemy battlefield and combat initiates, Volibear's attack trigger goes on the chain targeting three of the units at that battlefield. In reaction, the defending player plays Flash moving two of the three units back. That player cannot then target the attack trigger with Repulse, which reads "Choose a friendly unit at a battlefield. Counter an enemy spell or ability that chooses it and no other friendly unit." If the defending player instead played Heedless Resurrection twice, killing the two units, Repulse can legally target the attack trigger, because two of the targets have changed to a non-board zone.