What I find interesting is that you are mentioning this has happened over the last few months, which would put your sister's pregnancy at 5 or 6 months when it started? So, at that stage, your sister's pregnancy would be visually obvious. Has Zumi seen any other pregnant women and acted tense around them? I'm kind of thinking out loud here, and am not the most dog knowledgeable person here. I'm sure someone will come up with good ideas and solutions.
I have heard of dogs responding to pregnancy hormones. If this continues AFTER the baby, you might want to get her to come over if possible and be his only food giver. Failing that, always bring uber yummy treats.
Well Fran, Zumi seems to be fine with me and my own pregnancy. I am due March 30th… Zumi loves my tummy! and does often curl against mine and rest his head on it. though i will say that we (my sister and I) are carrying very much differently. Her pregnancy is VERY visually obvious, whereas I am not as visually obvious at all.
I suppose it could be her look, and her little waddle-walk, but i really don't think so, as he reacts so strongly even if she is seated and a complete non-threat.
I don't have any help to share, but I hope others on this site will give you some good advice.
The behavoir you describe is similar to the way Ella treated almost everybody for most of the first year we had her (myself included). I have observed the "I will sit close to you and want to be petted, but I will run away when you try" behavoir before. Ella is a master of it. Your situatioin is more perlexing since it is just with one person.
My recommendation would be to build an association of whatever Zumi's favorite treats are and close proximity to your sister. If Zumi has favorite toys or treats he goes crazy for, reserve those items for your sister to present to him. Once he is contently chewing away on something, have your sister touch or pet him and see if he tolerates it better. If he knows any commands, give your sister the best treats and get Zumi to work for her. I think that is great way to make a connection.
But in general, give Zumi space and do not force things. A Basenji knows. Be careful with too much eye contact. Another option is to do nothing and tell your sister to utterly ingnore him at all times. Basenjis are smart and eventually he will figure out that she is not a threat and that she is part of the extended pack.
Did your sister ever startle Zumi? If one startles my boy, one is on his sh*t list for a long, long time, and his behavior toward that person is much the same as Zumi's is toward your sister. This has happened to us three times. All three times, I've had the person ignore him completely for weeks, then even when he starts to trust this person again, I still have them ignore him for a bit longer. When his suspicious behavior is mostly gone, we start in with thrown treats/praise, then treats from the hand/praise, then petting, and, finally, all seems well. It takes a long time for my boy to again trust a person who has startled him.
Did your sister ever startle Kumi? If one startles my boy, one is on his sh*t list for a long, long time, and his behavior toward that person is much the same as Kumi's is toward your sister. This has happened to us three times. All three times, I've had the person ignore him completely for weeks, then even when he starts to trust this person again, I still have them ignore him for a bit longer. When his suspicious behavior is mostly gone, we start in with thrown treats/praise, then treats from the hand/praise, then petting, and, finally, all seems well. It takes a long time for my boy to again trust a person who has startled him.
I love your comments, because it shows respect for your basenji and his limits.
thank you everyone for your comments and advise so far.
bcraig, yes I have been mainly just having my sister completely ignore him, and giving no attention o his naughty behavior. no help yet..
and gbroxon i did not even think about her maybe startling him! As soon as i read your post i called her and YEP! she did!
Apparently she came over early one morning to pick up some books and magazines when mom and I were at a Drs appointment. She had also brought her own dog with (Zumi has no issues with her dog still) and grabbed his food dish off the floor, even though it was empty, Zumi is food/bowl aggressive towards other dogs. I guess her unannounced entrance startled him quite badly, and then the attacker took away his bowl. this could most definitely have been his trigger.
Sister said he backed away from her growling, hackles up and when she walked nearer to him that he even bared his teeth then ran and hid behind the recliner chair in the living room.
I suppose i shall also be stocking up on cat treats and those little Natural Balance rolls. He will do ANYTHING for them. lol, just another item to add to her diaper bag. Yes he knows a few tricks, and commands. I will have her treat him and ask him to obey a few commands each time she visits here so that she can be recognized as a friend again and not a scary attacker.
THANK YOU SO MUCH! i would never have thought of that.
Oh, this is good news that maybe this can be fixed.
I too have had this problem with my 2 1/2 year old, entire boy, but with my 15 year old daughter…
He just one day decided that he was going to do the same thing your boy did, with the ears back, much lip licking. growling softly etc, etc... I actually put a thread about this on here... It was only happening to her, and while he was in the crate, BUT, when he was out of the crate, he would watch her every move...
It stopped as suddenly as it begun, but then just the other day, while we were taking updated pics of all the dogs, (to take with us to CRUFTS :D), he did it again, while he was on the table, even though she was holding the bait, which he was going 'bananas' for just a moment before. He was put away, and all is in unison again... I tell you he is doing my head in :(...
Im really glad you found the reason SenjiShowgirl, that Zumi was doing it... I hope that it all works out for your sister, after a little while ;)... I just wish I could find a reason for Saba's 'issue' 
...
And this is why this forum is so awesome!!!!
