Two of my three Desert Kings dropped their breba crop a couple of weeks ago, the only edible crop here. The small fruit had almost rot like brownish/black spot before falling. I don't know what could have caused it since the plants were stored in a cold cellar and I took all precautions for getting good breba. Now I have to take care of them for no gain this year.
The 3rd plant showed only 3 breba fruits (still tiny).

One thing I did last year after all the breba crop ripened was to remove all 2nd crop figs as they emerged rather than leaving them on (though I had read to leave them on). I am not sure if that could be any factor in dropping this year brebas. However, it is most likely the rot-like brown (then black) spots that caused the abortion of the fruit. What is your opinion?

My opinion is the tree is not old enough to keep the fruits.
I had 50 fruits on my 6 years old and 30 developed normal while 20 never grew but stay very small and incipient turned blackish just like yours and fell out on 1st of May.
Of course another cause could be that the embryos were damaged during winter,and they fail to develop later,and fell out.
Last Year it had 10 fruits only 4 grew and 6 fell out just like yours.
So it is the strength ,of the tree that makes it drop or not,in one instance or the Embryos were partly damaged by frost in the winter and fell off later,in the second instance..
And in pot is not easy to keep a tree in maximum strength shape.
That is why Adriano keeps his Desert King in ground in Canada.
Of course it is near to impossible to keep the Embryos alive,trough the winter,on an inground tree in Canada, but :::HE DOES.
Here is my Desert King,6yrs old in pot .
It has fruits in stagnant stage the size of a golf ball now.
This is in my opinion the best Breba fig there is,but:
All breba figs are difficult to fruit in cold climates.
That is why I only grow it as an experiment and not a base fig.
My base figs are early main crop figs.

Ottawan, my DK is giving me its biggest crop ever. So far I think a few may have dropped but plentiful still remain on tree.  Of course my DK is an in-ground tree under 6ft tall with a spread over 5ft. I noticed DK is amongst the few variants that produces its crop of brebas later. I believe your DK brebas drop is mainly due to pot culture & weather related. Likely pot culture is not ideal. Did you get cuttings of  DK from Michael?? He has a good tree. Last year his tree may have given him  400 figs or more. Not a very big tree but well branched & in-ground. Also if my memory is correct Herman in one of his posting recommended not to pinched off DK main crop figs. I knock them off in late Jan & they come off real easy. Should be harvesting my DK in August.
 

I asked this because I had good breba crop from my Desert King plants last year and was expecting a repeat performance but it did not happen and do not want to repeat the conditions that caused the breba abortion if I could avoid. Those brebas were good!
Somethings that might have been different this year were:
1. Plants root-bound in pot? It is the 3rd year in pots and not root-pruned yet,
2. Did not follow advice not to remove the 2nd crop figs (for experiment),
3. Brought too early to the garage from cold cellar where they were safely hibernating at (under) 45F
4. The concrete cellar has good humidity and the ceiling (top exposed to outside) has frozen ice in deep winter though the room is at around 40F and not colder and sometimes the ceiling drips moisture drops on the plants

But most probably, as Herman mentioned, the brebas got damaged sometimes during embryo stage, they developed to a cherry size with a brown spot on each breba length-wise and all dropped within a few days so there was no blaming of the squirrels since the dropped fruits were lying on the ground.
Well, there is a chance next year after this summer, fall and a winter with deep freeze, a lot of snow, slush and fig storage for winter and back again.

My one year old DK-RT from Encanto cuttings set a dozen breba , but now has lost a few. I think I am down to seven now. Hope they can hold on so I can give it a try.
Should I pinch new growth at six leaves ?
I know geofiz mentioned pinching terminals just before bud break in Spring and again in late July.

Kerry
Pinching is for expediting embryo formation on new wood. Desert King useful crop breba grows on last year wood so pinching on Desert King is not going to be of much help in mine or your areas where the 2nd crop is not edible (needs pollination by that special wasp).

Hi Ottowan ,
I was thinking of the pinching in terms of the resulting branching producing more wood this year for next years breba crop.
Do you think waiting until late july to pinch, as geofiz mentions, is better than pinching at six leaves to get the desired branching for next seasons breba sites ?

I pinch at either 4th or 5th leaf. Geofiz advise is good -- very informed fig friend and a 1st class fig teacher who taught me what works in my zone. I believe pinching in my zone at 4th or 5th leaf also helps in hardening new wood for winter.

In my zone I usually starting pinching at 5 because I have noticed that the 1st leaf node frequently does not show an embryo. Later in the season I start pinching at 4.

Herman
Last year at the end of June I had similar size breba (as on your tree)  on my Desert Kings (alas not this year).

So Paully , you are pinching at 4th or 5th leaf on DK ?
Just wonder why Geofiz advice is to pinch late July on breba types.
Really enjoyed the paper Geofiz wrote on growing figs in cool climates.

Yes I pinched at either 4th or 5th node mainly for following reasons:

a. I do not like the nodes to stretch too far apart.
b. I want to keep tree low & spreading(more branching) early. Translate into
    more figs. I don't want to climb a ladder to pick figs & I can protect tree
    easier from birds.
c. I want to harden wood sooner as my zone weather can hit below 30*F
    by 1st week Oct.

I think Geofiz advise on pinching late July is more related to hardening. Weather in our zone starts to cool down rapidly by Sept. Geofiz is well read on figs -- french & ital and has been an excellent teacher & fig info updates.

I specifically kept a 2nd DK tree so that I can prune hard over alternate years. DK is so far the most reliable variant. I hope Dauphine & Grantham's Royal
would do well in time. Also, I am trialing RdB, Gino & MVS. I have another variant called NEBO that ripens main crop -- produces celeste size figs but less flavorful & sweet. This may do well in a zone with higher heat units in late Sept/early Oct. I also get a fair size main crop from Latarrula & Longue d'Aout. Lastly, I do at times pinch before bud movement to get a head start in branching. I did that to almost all my variants in late Feb and the results have been happy. Some light fertiliser helps to spurt growth of new buds.

Paully ,
Thanks so much for your detailed answer.
It is a big help for me here in NH.