There were a variety of reasons why the Vinland venture ultimately failed. Harsh climate and scarcity of resources were key contributing factors, particularly the lack of high value resources that couldn’t already be obtained in Greenland (like narwhal ivory, for example). This was tied to a third reason, the small size of the ventures. There were not that many people involved and there were no big draws to increase interest. Iceland, for example, was basically free land with no native population and other places of Viking settlement, for example Ireland, were closer to hand and had resources to exploit. That ties into a fourth reason, the distance involved. Even jumping from Europe to Iceland to Greenland to Vineland, its a long way for people and goods and news to travel. This was complicated by a fifth issue, there appear to have been significant numbers of native people there. Scandinavians has already encounters and clashed with indigenous North Americans in Greenland, but their numbers in the mainland were more significant. The Scandinavians also made some faux pas. On one expedition they appear to have killed some natives. On a second they tried to build good relations and trade with the natives but the natives came in force a few days later and attacked them. One theory for this is that some of the butter the Norse traded may have been rancid or the indigenous people may have been lactose intolerant which may have led them to think the Norse were trying to poison them. In any case, the Norse alienated the indigenous people who were present in numbers that made their expedition quite untenable.

As for why not sail south, well, they had no idea what they would find there and after the failure of their efforts so far the logical corse of action would be to call the whole thing off. Vinland was an interesting venture, but given the numbers and resources available to the Norse it most likely could never have been successful. As for why they didn’t publicize it, there was nothing to talk about. From their perspective they’d found a fertile though otherwise unremarkable land but one full of an indigenous people who were numerous and could be ferocious if agitated. They had no notion of the extent and scale of the continent.

I highly recommend the Kunz and Sigurdsson Penguins Classics’s volume on the Vinland Sagas if you’re not already familiar with it and want to learn more. It’s a very accessible and compact volume that won’t break the bank and honestly a very fun read.