Bad, bad timing
Castle has had trouble finishing "Naked Heat", mainly because Beckett's gotten serious with one Dt. Demming and he's too proud to admit how he feels about her. So after Alexis has to cancel their Hamptons weekend plans, Castle asks Beckett instead. But, citing work as an excuse, she turns him down.
Its not until Esposito finally opens Beckett's eyes to why Castle is still hanging around the precinct that she dumps Demming and musters up the courage during Castle's farewell bash to confront him about her feelings...
...only to see him with his ex-wife/publisher Gina, who has decided to spirit Castle away to the Hamptons for the summer where she can stay on top of him to finish his book--without distractions.
And Beckett, thinking she's lost her chance, stays silent as Castle and Gina walk out of the precinct for what seems to be more than just a business trip.