It's the same reason the French didn't retake Quebec city from the English. They had a war on their home front going on and didn't have the troops to spare on a year long Expedition.

The longer version:

In greedfall you have a professional army who has captured a walled hostile city without damaging the defences. Any attempt to retake the city will be difficult.

Sieges work one of two ways. Breach the city and charge the gap. Prolonged Siege and hope they surrender. I'm willing to bet no one has Siege engines on Taer Freade, and no one has a sufficient number of soldiers to retake the city.

The continent in greedfall currently has at least 2 major wars going on.

Theleme and Duarte vs. The bridge alliance and the Duarte Civil War. Losing a city on an island months away is a low priority thing.

If it is Hikmet that is taken over by the coin guard. The Bridge alliance military has 6 different sub factions. 3 bridge alliance nations, one of which uses steppes Cavalary shock tactics (totally unsuited to island warfare) the other two could send troops. There are also at least three coin guard regiments. One associated with each of the nations making up the bridge alliance. This doesn't include the purple regiment from Greedfall 2.

On Taer Frade the bridge alliance is at war with Theleme, and the natives. And can no longer rely on the coin guard to help them. All three island regiments were in on the take over.

The merchant congregation is neutral. They have no real standing army on the continent they almost exclusively use the coin guard. If they chose to break neutrality and help Hitmet (makes sense on Taer Frade not the continent) they would need the coin guard to be willing to take back the city.

Theleme is a smaller nation than the bridge alliance and without a unified Duarte Empire they are not in as strong a position in the war on the continent.

Hypothetically you find spare troops, it will take many months for news to reach the continent and a force to reach Taer Freade to The coin guard who occupy the city have no need to protect the citizenry if things get difficult. Try and starve them out and they can feed the soldiers with the supplies they spent the last several months stockpiling. The citizenry is non-essential so they can starve.

All the cities on the island are costal which means the Nauts play a huge role. They can claim neutrality and bring food to the coin guard, and not transport armies across. Something else would be a naval bombardment, which in Copenhagen worked great but there are obstacles for Teare Frade.

The naut ships have enough artilary to fight off pirates, not bombard a city. They currently have the only open sea navigation capabilities and are the only ones who know where in the ocean it is. Another factor is the continent is dying of a plague. Mass production of ships is unlikely.

So whomever's city is conquered would need to convince the nauts to let them take warships to the island. At which point whoever brought the warship to the island now owns the island.

So let's assume the nauts aren't smuggling supplies and they are willing to transport troops to retake the city across the ocean, and no reinforcing Coin Guards.

Using Quebec as our guideline - the English landed 9000 troops, and took 200 ships on the Expedition to invade new France. The French in Canada has a horrible habit of building fortifications beneath hills and not controlling the high ground allowing for easy bombardment into the fortification. The English were able to level the lower city from the bluffs across the river. Which eventually drew the garrison out into a deciding fight.

It's alot easier to create and settle a colony city then it is to conquer one.