A Cuban wealthy elite became exiles in Miami, and a strong political force in their own right to put pressure on the government to keep the embargo in place. That coupled with the domino theory that the US foreign policy followed at the time they couldn't allow a successful post-colonial country exist peacefully outside of their sphere of influence. After the embargo had been in place for so long America only can lose by removing it unless they get some market access concessions from Cuba in return.
In Ireland's case the UK needed Ireland as a supply of livestock to feed their population so while the autarky hurt the Irish economy most people were poor farmers anyway so it didn't make a whole pile of difference while in the UK a rise in beef prices hurt their emerging middle class. Overall the amount of money involved was relatively small and since the Irish central bank was still linked to the Bank of England, Irish fiscal policy could still be tangentially controlled by UK monetary policy to keep trade flowing, without having to resort to physical force.
In reality the reason Ireland didn't face any sanctions immediately after "independence" was because it was mostly token independence where the economy was still heavily intertwined with Britain and little industrial development took place. This was maintained between 1923 and 1932 as the status quo benefitted the large ranchers and middlemen whose side won the civil war.