I sometimes have trouble with impatiens in plastic containers, but not in plastic hanging bags. I don't know what the trouble is when they die shortly after setting out.
Once they get good root establishment, they are ok. I think it helps to have plants a little larger when transplanting impatiens and go easy on watering at the start.

Go back to the wooden pot?!

It's very likely some combination of a less than ideal potting soil (retaining too much moisture, too many organics breaking down to impede drainage), the substitution of the plastic container, which doesn't 'breathe' like wood, and too frequent watering. I've grown an assortment of shade loving plants in plastic containers many times over the years without problems.

Water meters tend to be rather significantly inaccurate, so I'd not use them as good indicator of when to water. Test with your finger - when the soil feels dry when you poke your finger in all the way to the third knuckle, it's time to water. Or when your plants tell you :-) Plastic containers in shade will not dry out nearly as rapidly as a wooden one will, simply because the plastic doesn't breathe or allow evaporation anywhere along its surface as wood does.

And make sure you are working with a very high quality potting mix that doesn't have too high a percentage of organic matter but a good amount of drainage encouraging additives, like pumice, perlite or Turface. The Container Gardening forum can help you with recipes if you need some. Even a 'professional grade' mix will vary a lot in quality and texture, so no guarantees with just that description on the label.

I don't know the answer to your question, but I can say CT in general last year was extremely wet...Our garden only needed watering twice, compared to some years we had to water once a week.