The year interval between the first Nephite initiative and this stand at Teancum suggests that the initial foray that was defeated created a rapid retreat. That rapid retreat was followed by the Lamanite/Gadianton army. The Nephites stopped at Desolation, but with the pursuing army on their heels, they had to rely on existing defenses, which were inadequate. After the retreat they stop at Teancum.
This gives us a picture of a Lamanite/Gadianton army in Desolation (the first city north of the narrow pass) and the Nephite army at Teancum. The result of the Lamanite/Gadianton attack on Teancum is different, and it appears to come about one year later. It would appear that between the conquest of Desolation and the attack on Teancum, the fighting ceased in typical Mesoamerican fashion to allow for planting. When hostilities resumed, the Nephites would have had more time to strengthen the defenses around Teancum, and those efforts were successful. Of course it might also be that Teancum was already a larger, better-defended city, but the timing suggests that there was a respite where the Nephites could recover.
When the Nephites counter attack, it is now the Lamanites who have a tenuous supply line, perhaps exacerbated by the narrow neck of land. While the Lamanites had a supply system south of Desolation, it had to come through the narrow neck, implying that it would be restricting to a supply column. The supplies would be available, but stretched out for longer, and therefore take longer to arrive. With just the single city north of that point as a defensive position, and with the likelihood that they had attacked after planting but before harvest, the Lamanite/Gadianton army would be in a position of tenuous supply. Mormon gives us little details of the retaking of Desolation, but the supply-line picture suggests that Desolation was probably given up quite easily in a strategic retreat.