My tri boy lost hair in spots his first winter with us. I assumed it was a food allergy, but my vet told me most skin problems are caused by environmental sensitivities. Sure enough, I finally realized his problem started in the fall when the furnace came on; His crate was right beside a furnace grate. When I moved his crate, the hair grew back. All of which is to say it'll take some detective work to figure this out.
It does look like a contact dermatitis, 'tho! From the location of the problem, I'd ask if your B spends a lot of time lying on the carpet or his blanket in the "frog" position. If the carpet is wool, has rug shampoo or deodorizer powder residues, a rash could develop in that area. If he "scoots" across the rug on his tummy, it could even be rug burn…If his bedding has accumulated a lot of dust mites or was washed in strong detergents without sufficient rinsing, or a fabric softener was used that could trigger an eczema-like rash, and licking of the area would make it more chapped.
Ladybasenji, where are you in Quebec? Montreal? We have a place in Gatineau (Aylmer sector) and one of my dogs might even be related to yours. You're experiences with your girl remind me so much of my first basenji, about 20 years ago–it gets easier, I swear! Let me know if you'd like help with Lady--they're nothing like labs and will never be "obedient" but there are tricks for training them : D
Try feeding her bran cereal (with NO artificial sweeteners listed in the ingredients!) softened in plenty of water an hour B4 a walk. This has helped me correct crate/indoor pooping issues with several puppy mill fosters by increasing the urge to eliminate; They poop outdoors, giving me a behaviour to reinforce. She might be a shy pooper, too–if you can, find her a screen of tall grass or brush for privacy, don't interupt her with praise or be loud offering it, and never yell or strike her for pooping indoors...many dogs won't potty within sight of their owners for fear of being reprimanded.
At 1 yr old, I don't consider B's 100% reliably housebroken–there's still a lot of things that can cause accidents: rain or wet grass; the lingering odour of a predator in the area; an upset in routine; travel; food changes etc. My dogs have always been confused by seasonal changes for their first few years--they just get accustomed to pottying on grass in daylight, then overnight it's snow and short days! While I've never found B's to be especially empathetic, it's possible the change in routine or your divided attention caused by the death in your family could affect your dog.
One thing that's always worked for me is what I call a "Bran Bomb": a small amount of very high fibre cereal softened in plenty of water fed just b4 breakfast. It increases the urge to eliminate. It's helped me get a number of fosters on elimination schedules. Just pick a brand low in sugar and with no articicial sweeteners, which are toxic for dogs.
Also, patience is key--many of us are focused on getting to work in the morning, yet some dogs--depending on food--require two bowel movements in the morning.
I'm the original skeptic, and believed half-heartedly in heaven until my girl–so much like yours!--passed away. Now, I believe whole-heartedly. Listen with your heart--if you're as lucky as I've been, you'll hear her. I'm so sorry for your loss...be kind to yourself.
Do you live in the country? Is it possible your dog is hearing wolves, coyotes or coyo/dogs? I've noticed the time you mention is when packs in my area become vocal, although it never seems to bother my dogs. It's possible your dog is reacting to something only she hears, and I find wild canid packs are most vocal in late fall/winter/early spring. I often hear them around 3pm on cold, clear nights when leaving for work, it doesn't have to be a full moon.What DOES bother my guys is the presence of bears, fisher cats etc around the property. If you have lynx or cougar in your area, they really seem to stir things up.
Try locating a breeder through your area kennel club. Having said that, Basenjis are NOT hypo-allergenic. In fact, a leading cause for them being surrendered to rescue is allergies.
Also, what a breeder might not tell yoi (some are interested only in sales) is that basenjis demand a huge amount of attention, and if they don't get it they find their own entertsinment. They don't do well when left alone, so it's wise to keep two, and while they're beautiful dogs if their looks are the chief reason you're interested you should really do more research! They can be really frustrating dogs to own!