Rambutan is more tropical than longan or lychee, and the seedlings need consistently warm temperatures.
Have you considered a heat mat and growing them inside an enclosure under a grow light?
It's not uncommon for lychee or rambutan to show stalled growth at about 5 to 9 inches. Before that the little plant is relying on energy stored in the seed.
Also I'd use a soil type that retains water well, because you need the soil to remain constantly moist.