Ever wondered how the shields in Warframe worked? Ever though to yourself, Why is Penetration so easy to block with a shield? That makes no sense!
Well I have an answer for you.
This is something that I did a worrying amount of research on. I am a Smith, and an Engineer, and I am weird. So, To fulfill all of your questions (Hopefully) I have made & tested this theory.
Looking at how the shields function, with a good resistance towards puncture and slash damage, and a very bad resistance against impact damage, there is really only one way that they can possibly function. They can't be a stereotypical "Shield", like a large flat sheet, as that would be better against impact damage, therefore they must function by coalescing energy around an object, which would be very good against puncturing weaponry, like a bullet, as there is very little to deflect, and thereby it wouldn't need to expend as much energy. This also explains why the shields are very good against slashing damage. They are still just shoving against a small area, and therefore they have little trouble. However, when they encounter something with a larger surface area, they can't deflect it as well, as they will have to coalesce much more energy to shove it away. Thereby, it's not that the shield is really "worse" at deflecting Impacts, it just has to expend more energy, making it less cost effective to deflect.
So, In summary, it's just a matter of Mass. Slash and puncture weaponry should have less mass, while impact should have more mass. Any status effects that injure shields, can also (sortof) be explained. Batteries, which presumably power the shield, work much worse in the cold. Heat, unless it's overwhelming, doesn't do much to batteries. As was pointed out in the comments, toxin and gas is probably just ignored by the shield, because it is neither solid or plasma. Blast damage is spread out, but large, so it hits much of the shield. Radiation just messes with it.
(Made from Prior Knowledge, Physics, Science, and the brain of a madman)(This is totally unconfirmed, just a brain-child of User: dragon489902)
(Yes I had a "How To" section with how I did this, but it was flawed and I don't really want to spend another four paragraphs trying to explain how I tested it.)
Hope this clears things up!