Kenmore is decent stuff. I actually prefer them to most other brands because they typically only rebrand items that have been reviewed to be decent quality. SO the manufacturer will make the product and Sears as well as most other repair people will support it. I've had good luck with them. (4 fridges, 3 gas ranges, 2 dishwashers) I've moved a few times and had a rental unit...all Kenmore appliances.
The way I look at it, all fridges with digital displays are suspect to problems these days. (In other words, if you see LED displays anywhere in the fridge or on the doors) That's not to suggest you will have problems, but they started putting more complex electronics in the fridges about 8 years ago. The main controller boards cost $150+ to replace, so many repairmen will replace that part last after they replace everything else.
My parents bought a brand new Frigidaire from Lowe's. It stopped cooling weeks after they got it. 3 days later, they finally got a repair guy to show up (Lowe's wouldn't replace it) and it took weeks before he was able to get the right parts swapped out. A few years in the future after out of warranty, it started having problems again. I'm not bashing Frigidaire, but all manufacturers are making all the parts modular and a few power surges or static discharge or moisture can screw them up quick.