endlessly; without limit; ad infinitum
Used when something continues without any bound or end, often with a negative or critical nuance. Common in both formal and everyday contexts.
His demands continued endlessly.
Spending money without limit is dangerous.
際限なく focuses on the lack of a limit or endpoint, whereas 止めどなく focuses on an unstoppable, continuous flow.
From 際限 (さいげん, 'limit' or 'end') + なく (adverbial form of ない, 'not'). The compound 際限 is itself from 際 (さい, 'edge' or 'boundary') and 限 (げん, 'limit').