At the end of the Second World War, why were there still so many groups of German soldiers that kept fighting?

Because:

One, they didn't know the state of things. Germany was still telling them they were winning. It's not like they'd just take the Allies word for it that Germany was losing.

Two, by the bitter end, Germany had already exhausted most of its experienced troops, so Germany drafted 12-, 13-, 14-year-old boys in its last ditch effort. If you've ever met a 12-, 13-, 14-year-old boy, you know that they each think they're invincible, and for their friends, for their team, they'll sooner die than give up, but they really don't think they're going to die. Boys that age haven't even developed their frontal lobes yet and so haven't developed the logic area of their brains, so expecting a logical response from them, one that has them giving up when for years they've been told they can't lose because they're the Master Race, that's just not in the cards, wasn't ever going to happen. It was actually quite difficult at the end because of this, because Allies were seeing through their guns' scopes kids, boys, boys often still prepubescent because of malnutrition, and were refusing to shoot them, so at the end, those boys actually fared fairly well as the Allies went about trying to capture and detain rather than kill kids who were perfectly willing to shoot and kill them.

Some units of Heeresgruppe Mitte (Army Group Centre) in Czechoslovakia fought on for several days after the official surrender at 0001h, 9 May '45. They were surrounded by Soviet forces & tried to break out to the west so they could surrender to the U.S. Third Army. As the Soviets weren't party to the 1929 Geneva Conventions on Treatment of Prisoners of War, they knew that if they tried to surrender, they'd be either summarily shot or treated brutally. A large number were killed outright by the Soviets & about 1/3 who were captured by the Soviets died by various ways in custody. Many were held until 1955. Pretty damned good reason for wanting to go on fighting, in my opinion.

Germans had been taught that the Allies were monsters and that they would be treated very badly if they were caught (there was actually some justification for this - Allied soldiers were not angels). The choice between fighting for your country and dying, or being caught and killed, is no choice.

because they fanatically believed in Hitler and also thought Allies invaded their country

Why especially in the Western Front? The Eastern Front was by far the bloodiest and cruelest. The Krauts preferred surrendering to the Americans and British, certainly not the Soviets.

Anyhow, that answers your question why the Krauts fought like hell against the Russians... fear of retribution if they were captured.

the Germans were indoctrinating children at school, a dogma in the final days these were fighting children 13/14.15 plus old men ex soldiers those who refused to fight were hanged as cowards in the streets and left for all to see by the SS a dogma is easily consuming these kids thought they were heroes there is film of Hitler addressing the ranks of these kids pinching their cheeks like a loved one its abominable

"You always hear story after story of ..." Perhaps I've been asleep on the job, but I've never heard of even one such story pertaining to German troops.

They were defending their home, their way of life, their moral integrity, and their people. Most people don't understand that because they've been taught that Hitler and the Nazis were evil and wanted to take over the world. Almost none of what was said about Hitler is true - that was just the way the Allies sold it to their own people to maintain support and to justify the crimes they committed against the German people.

The most devastating of the propaganda was the "extermination of 6 million Jews" that was quickly believed by the people after reading articles in the media for 18 years about how "6 million Jews were being persecuted and threatened with extermination". This Zionist "theme park" began in 1915 long before the world ever heard of Hitler - and yet, when he's accused of exterminating Jews in 1933, a connection was made that became a false historic fact that labeled Hitler as an evil madman for all time.

Perhaps you would care to share a few of these stories with us, I can't recall hearing of any,,, other than the German weather unit posted on a remote Arctic Island that didn't even know the war was over or maybe the Battle of Itter Castle,,, when U.S. and German army regulars teamed up to fight an S.S. unit, that was right at war's end,,,, or maybe you're thinking of Operation Werewolf,, which never amounted to anything more than a propaganda campaign that quickly died a quiet death.