This is the 8550th most frequent Russian word.
обещаний
"Обещаний" is the genitive plural form of "обещание," meaning "promise" in English.
Here, 'обещаний' is the Genitive plural form of the noun 'обещание' (promise), used to describe the absence of promises being fulfilled.
Ещё один день прошел без выполненных обещаний.
Another day passed without fulfilled promises.
In this case, 'обещаний' is again the Genitive plural, indicating the quantity of promises that were expressed.
Он произнес несколько обещаний на собрании.
He made several promises at the meeting.
Here, 'обещаний' is used as the Genitive plural with an adjective ('неисполнимых'), forming a descriptive phrase about the nature of the promises.