If I abandon a Counter Spell, can my opponent play that spell to counter mine?

Yes, it is possible for your opponent to play the spell again after your Abandon resolves.

According to RiftJudge FAQ #9457, the chain is not an immutable block that must resolve all at once. Instead, it is a sequence of items that resolve individually, and players receive a window of priority to add new reactions after each individual item on the chain resolves.

Sequence of Events:

1. Initial State: Your opponent plays a spell (let's call it Spell A) targeting one of your spells.
2. Your Response: You play Abandon targeting Spell A.
   • Chain (bottom to top): [Spell A] -> [Abandon]
3. Resolution of Abandon: The chain resolves LIFO (Last-In, First-Out). Abandon resolves first. It counters Spell A and returns it to your opponent's hand.
4. Priority Window: Because the chain was resolved one item at a time, the game enters a priority window before the game state returns to "Open." Since Spell A is back in your opponent's hand, they may play it again targeting your original spell.

This is possible because Abandon is a [Reaction] spell, and the game grants a priority window after every item resolves on the chain, allowing players to play new reactions (or in this case, a spell from their hand) before the original target spell (your spell) resolves.