I left some outside once, and it thickened up quite a bit, it also changed colors slightly. This was in a jar that I had poured some extra in, so it was only a little bit and I didn't continue to use it, so I can't help you there! I did bring it back inside, and checked it a day or so later, it seemed to thin out a bit, but I never opened it again, I don't think the color ever went away.
I buy it in pints, and have been using it, then hammering the lid back on, for a month or two now, then bring it back inside, it's just as thin as it was when I got it, so I don't think the container matters.
Of interest, I couldn't get the top off of a 2oz jar once, so I got ticked and poked a hole in the top, then dipped a bait in there as usual. It took four days to develop a film like this, must have been the way the air couldn't get in the hole in the top!