First, Ireland wasn't a distant colony like the others mentioned, the 1800 Act of Union made it part of the United Kingdom of Great Britain and Ireland. Just like England, Scotland and Wales, MP's elected in Ireland took their seats in Westminster. An uprising in Ireland wasn't viewed as colonists going native trying to break away from the Empire, it was an integral part of the United Kingdom trying to break away. During the War of Independence the UK deployed demobbed British soldiers to Ireland as part of a police force and never formally involved the army. They painted the conflict as being simply a criminal situation. Deploying the army would have been an admittance that the United Kingdom was in the middle of a civil war.

Proximity and size meant it was easier for Britain to control Ireland than it was for the other regions you mention. The likes of Canada were given Dominion status due in part to their distance from London and the difficulty of direct rule. The UK was caught off guard during the 1916 Rising in Dublin but was able to deploy 16,000 troops to the city within days, most of them being transported directly from Britain.

Control of Ireland had strategic consequences for the UK. In 1796 14,000 French troops had attempted a landing in Ireland but were unable to do so due to bad weather. In 1798 a rebellion broke out and 1,000 French troops landed at Mayo and a larger force failed to land at Donegal. The 1800 Act of Union was forced through the Irish Parliament to bring Ireland under closer British rule and a number of Martello towers were built along to the coast during the Napoleonic Wars. The 1916 Rising leaders had secured weapons from Germany but these were captured by the British before they could reach shore (the ship carrying them was scuttled near Cork harbor) and there were fears that Germany would attempt a landing. In 1918 British authorities in Ireland attempted to arrest 150 members of the Nationalist movement, capturing about half that number. Though they had no evidence they genuinely seem to have believed that the Irish were again collaborating with Germany and that plans were in place to land up to 70,000 German soldiers. 26 of the 32 counties of Ireland gained Free State status in 1922 but a number of "Treaty Ports" remained under British control due to their strategic importance. These were handed back to Ireland in the 1930's and during World War 2 there were some brief calls for them to be returned to Britain for the duration of the war. Naval ports in Northern Ireland produced ships for the war and many US soldiers were based there. The United Kingdom assembled "Plan W", a planned invasion of Ireland, at the request of the Irish government, in response to a German invasion.

Imperial pride had a lot to do with it as well. Ireland fought a War of Independence against British rule from 1919 to 1921. Since 1800 Irish politicians had been arguing for Home Rule, limited self government within the Union, but this was continuously refused. The 1916 Rising and World War 1 change opinion massively in Ireland in favor of a Republic. If Britain wasn't willing to give Ireland Home Rule they defiantly weren't willing to give that! Ireland was one of a number of Imperial possessions, British or otherwise, that fought for its independence in this time period. Britain's power was waning and it didn't want to speed up this process by allowing Ireland to go easily. Anti-colonial struggles following the World War convinced Britain the days of its Empire were over and this was reformed as the Commonwealth of Nations in 1931, of which the Irish Free State was a member and remained so until the Republic of Ireland Act 1949.

Since 1922 the the six north easterly counties of the island have remained part of the United Kingdom of Great Britain and Northern Ireland. The plantations, where land was stripped from the native Irish and given to British settlers, had been most successful in this area and they had a strong Unionist population, though they were a tiny minority on the island overall. They had resisted Home Rule and threatened civil war to remain part of the United Kingdom. The party governing the UK today is officially the Conservative and Unionist Party (often just refereed to as the Conservatives) and they strongly supported the Irish Unionists. Following the partition of the island they have supported Northern Ireland's place in the Union and continue to do so. The area has limited strategic value in the modern world and has been heavily economically deprived under British rule but is still defended by them as an integral part of the Union. The Troubles, a 30 year armed conflict mainly involving Nationalist and Unionist Paramilitaries, Northern Ireland and British state forces, ended with the signing of the Good Friday agreement in 1998 which says that Northern Ireland will remain part of the United Kingdom until a majority vote otherwise. Changing population dynamics and Brexit are causing many to call for a boarder poll on Irish reunification, something the Conservatives want to avoid.

TLDR: Ireland's proximity meant it had strategic value and made it easier for the United Kingdom to impose direct rule on the island. As a constituent part of the United Kingdom of Great Britain and Ireland loosing it had deeper political ramifications than far flung parts of the Empire.