My loose translation would be
I already gave up on the diet after 3 days.
And a more precise one
As for the diet, I regrettably stopped it after 3 days.
From my understanding, で is used to say "after". But で usually marks the method by which an action occurs.
So, is my translation "after 3 days" correct? Can you name a more precise translation for the example? And what is the semantic of で in respect to this example?