You most definitely need to keep the soil moist. I'm assuming they are in pots? The general logic of keeping them cool and dry in winter is for when they are planted in the ground. In other words, they shouldn't be irrigated in winter, and less humidity is desirable. That doesn't apply if you have them in pots.
I'd imagine that temperature isn't a problem, as long as it's above 40 degrees...which it must be if all of those other plants are doing well.
The only other thing I can think of is that the leaves do have a life expectancy, and when new vegetative growth starts, the older leaves start to brown and drop off. Generally, the vegetative growth should show up in time to replace the older leaves, but if the temps in your greenhouse are too low, that new growth may be delayed a bit. Vegetative growth initiates around 70 degree temps.
I would strongly recommend that you maintain a good watering schedule. The hardest part for me is keeping my lychees moist but not drowned. I try to water just to the point of absorption, but not saturation. You may want to give them a good drink for the next week, then start a regular schedule. I hope that helps.

I agree with north tree man. I don't try to keep my lychees on the dry side in winter like some other plants. My lychee in the pot seems to do better with moist soil year-round. This is made much easier with a fast draining, large particle container mix. For a complete essay on that, check out the seminal thread on the Container Growing forum by Tapla entitled "Water Movement in Containers," now in its fourth iteration. I also sometimes use a strip of old towel in the bottom of the pot to wick out the water table so I can water fearlessly.

SB

Thank you both for your advice. I will water them on a more frequent basis and hope for the best.

SB, I'm curious...What do you do with the towel strips. Are they on the bottom of the pot and then trailing up the side of the pot and over the top of the pot? I wondered about the wicking part of the long soil post.

Thanks for the info.
Tj

As an update, my Lychee has put out new growth and appears to be recovering well. My Longan, although still having green cambium, has not budded out at all. I think it is done for. Would any sort of root stimulator or other compound be of any use at this point?
Or should I expect to wait longer for new leaves?

Glad to hear the lychee came back. As for the longan, you'll probably need to take the "wait and watch" approach. Maybe 'DGHays' will stop by and give some insight...he seems to be the longan expert around here.

I agree with people above its almost certain to be a watering issue, and also that there's not much to do except water it the correct amount now (don't over-correct), and hope it sprouts its leaves. You could attempt to plant it in a good spot to see if that helps, and dig it back up at the end of the summer. Irrigation and fert is much more difficult in container gardening.

Gary

Well, I've continued to water the Longan in it's pot. Today I found a new sprout and other buds on its branches, so it is coming back. Thanks everyone for the help. Assuming it grows back to a regular sized canopy this year, what is the recommended fertilizer and schedule to follow for this tree?

Hi. I'm glad to hear your longan is coming around. Here's a fertilization, etc. schedule as it relates to longans in Florida (bottom of the page):
http://edis.ifas.ufl.edu/MG049