Dormant cuttings of several varieties (two cuttings per variety) that I obtained in first week of December 2013, rooted well in SM within 3 weeks.
From December 18 to December 27 I was potting them into 24 oz clear plastic cups. One half of cups were constructed as mini SIP. One cutting of each variety went to mini SIP, other to regular cup.
The medium is made of 1:1:1, Coarse perlite, coarse pine bark, MG seedling/cutting mix.
Medium pre-moistened a day ahead of potting, tested in cup to barely produce a dew on the wall of the cup.
This resulted in a tremendous root development followed by good leaf/stem growth. Niagara Black, NdC put 3-4" shots in 4 days. Roots reached the lids of the cups and turned downwards, side roots branched nicely. All cups were in humidity bin with a bottom rack and under fluorescent light. Room temperature 23 C. Lid was on overnight and off for a couple of hours daily.
Condensation on the walls disappeared after 3 weeks and I administered first watering using syringe to feed water through SIP straws. 20 ml per SIP. Other cups were bottom soaked for 2-3 minutes to absorb water.
Over the weekend the lid was left closed on humidity bins. After opening the lid leaves went droopy on most of the cuttings, primarily on thin ones. Over the course of the week, managed to keep leaves perched up by keeping the lid on the bin.
Eventually they wilted. Upon examination of failed cuttings discovered rotted bark at the base of the cutting on the thinnest cuttings. Growing Medium appeared on the too wet side.
Also found completely rotted cutting while medium appeared normal to dry.
Some cuttings went through stage of shrinking already swollen green buds and drying out.
Upon uprooting these, I found no rot at all, and growing medium did not appear neither too wet nor dry.
Although buried up to top node, upper half of the cutting was dried out. Roots were well alive.
So found all kinds of failure modes.
Only the thickest cuttings of BT, Celeste, RdB and NB are still doing OK.
Are my cuttings deprived of oxygen? as a result of lid left closed for 60 hours?
 

Even when you think they are dead, they prove you wrong!  Best to care and leave them alone, uprooting them causes stress. Even the most profficient growers have a loss percentage. So, it is a challenge each time.  Also depends of the life condition the cutting had stored. 

when you say humidity bin lid, are you taking about those lid on the cup or something over the whole set up?

if it's the lid on the cup, i can see how it failed. if it's something over the whole set up, chances are you are airing them out too long. start out with 5-10 min and slowly increase to an hour.

once the cutting above the soil mix dry out, you are done. cutting under the soil will rot.

Hi Can_smokva,
It can be a lack of co2 in the humidity bin and/or a lack of light.
Are you giving them fertilizer ?
Are you giving them lighting ? natural /sun ? bulbs ?
The bigger cuttings are now shadowing the weakest - you "need" to put those in a separate humidity bin .

I think, that you are pushing them too much, and the rooting system can't handle the top growth.
I have 3 cuttings at home and their leaves are shorter and thicker than the ones on your cuttings.

Jdsfrance,
thanks for suggestions
The light should be fine because it is identical to the other light under which previous small batch of survived cuttings from back in October is thriving!
No fertilizer given.
My biggest confusion is that under the "same" conditions within the same humidity bin, some are failing from being too dry, others from rotting!
Your observation about the growth stands, they are lenky since they grew in 3 days 4 inches and stopped there.
This is all new to me. I'd like to learn the causes.
for one I suppose different cuttings need different treatment.
in the future will be more careful and group them accordingly.
Pete,
I have found that those that start to decline (drying, rotting, mold) are almost impossible to stop.
Those I uprooted, I discarded. Eventhough some may not have been dead, they would fail in a week.

can_smokva

We always have tendency to rush to water newly rooted plant when we see the soil top appear a little bit on the dry side. I have stopped doing this and have not seen a rooted plant dying out as you mentioned (after watering) for a long enough while.

I moistened the ProMax potting soil, squeeze out the water as much as I can; I place the cutting from the baggie method in the 24 or 32 oz clear jar and then gradually pour the potting soil around it loosely (granulating it with fingers) and fill up the jar as required, at the end giving the jar a gentle tap on the ground. I keep the jar in a plastic covered area with 60~70% humidity and 73C~75C temperature. I restrain myself from watering if the plant in the pot is growing fine even if the soil on top looks a bit on dry side sometime or a month or so. I believe there is enough moisture in the soil volume to sustain the  growth; if not the plant leaves will let you know in advance enough before damage. Then make sure not to over water.
If you feel that the pot has been over-watered, use wicks made out of tissue paper inserted into the holes at the bottom to gradually removed/drain extra water by keeping the pot a few inches high so the water from the wicks can easily flow out through the wicks.

Good luck.

Can_smokva,
My highest cutting success rates have been using the potting procedure that OttawanZ5 described above, prewetting the potting mix and tapping the bottom of the container to settle the mix around the cutting, maintains lots of air in the mix. I don't monitor humidity or use humidity dome once the cuttings are potted, and maintaining the temperature above 70 deg F. guarantees fast growth.

Your problem may have been too much moisture in the mix, which caused the cuttings to rot before they had a chance to callus.

last yr, i had same problem with few i took out of the bin too early, or air out too long. the cutting itself dries out, and the root rots in the end.

this is what usually happens to my green cuttings.

this yr, i did things little differently. basically, i kept them longer in humidity dome. it's working for me. i've kept greener cutting longer in the baggie until the cutting turned color. then i kept greener cutting in separate humidity bin. i air out the green cutting much shorter, and increase the duration very slowly.

winter is not over, so i'll find out if it truely works in about 3 months :)