mine actually do the same thing.
i thought mine was from not having enough water
but, i guess not.
im no expert at all, wish i could give you a better answer.
i can tell you mine went down to 0C I(32F) the other day
with no problems at all, and they are pretty small like yours, just a few inches tall.

you might want to give it a larger pot though.
Lychee roots need more room than other fruit trees i believe.
you might want to consider Mycorrhizal fungi, or worm-tea.

i had 8 seedlings, and killed 3 already
2 of them are over 1ft tall I(30+ CM)
the other 3 are smaller and barely growing.
i gave them all worm-tea and Mycorrhizal Fungi, but,
the ones in larger pots are doing better.

i read that Mycorrhizal Fungi doesnt last (or take hold?)
in small containers

i used a cheap potting soil, but added compost , peat moss, and a little coarse sand for drainage.

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on the link i have below,
i would suggest reading these pages...

15 Tips for Tips for Planting your Lychee Tree

5 Tips for Growing Lychee Trees in Containers

8 Essential Factors for Growing Healthy Lychee Trees

Lychee Tree Root System and Development

Inoculation with Arbuscular Mycorrhizal Fungi Enhances Growth of Litchi Chinensis

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The soil quality in potting mix is nothing like the original natural forest environment of lychee trees in Southern China. If you grow a lychee tree in a container, you must take measures to improve and rejuvinate the soil quality or your tree will slowly die within a few years. Mycorrhizal Fungi is a soil treatment that will increase the roots ability to absorb and distribute nutrients and water and innoculate the tree against many plant diseases and pathogens.
http://www.lycheesonline.com/containertips.cfm

Our observations suggest that in this soil-free medium, arbuscular mycorrhizal fungus enhancement of copper and iron nutrition improved lychee growth.
http://www.lycheesonline.com/containertips.cfm

Here is a link that might be useful: http://www.lycheesonline.com/lycheeinfo.cfm