interesting that they have pretty much no idea where it will end up, i thought they'd be able to estimate that a bit.
The alternatives occur because it is losing speed only very gradually with each orbit through the upper atmosphere. Tiangong-1 goes around the planet every 88 minutes, and one of those orbits will lose enough speed and altitude that the vehicle disintegrates due to heat or drag. It's just that due to variations in the upper atmosphere, we don't know which orbit exactly will finally tip the balance.
This is in contrast to a controlled re-entry vehicle e.g. Soyuz that washes off something like 150m/sec in a single engine burn to place it on an known and specific sub-orbital trajectory to get home.
I'd think there would be significant variation in that simply due to weather. If I remember right, the atmosphere expands quite a bit on a sunny day.
Solar flares and other similar events happen all the time. They're not really noticeable at ground level, because they don't appreciably affect the sun's visible brightness, and the density of matter involved is tiny compared to the atmosphere at ground level. But at the heights where satellites orbit -- where the atmosphere is already extremely tenuous -- solar and geomagnetic phenomena can have a huge relative effect.
The expansion of the earth's atmosphere due to heating effects has very much to do with clouds.
The proportion of reflected light is called the "albedo", which ranges from a theoretical maximum of 1 (a perfect mirror, or a theoretical white surface with no absorption) to 0 (a theoretical "black body").
White clouds reflect a lot of the incoming sunlight (have a larger albedo). Light that strikes the ground from a clear sky causes more ground heating, which causes more air heating, which causes the atmosphere to expand.
ATW, the Earth's albedo can range from about 0.9 (fresh snow on the ground) to about 0.06 (open ocean). White clouds can approach about 0.8.
Edit: the height of the tropopause (the boundary between the troposphere and the stratosphere) varies from about 9 km (over the poles) to 17 km (over the equator) due largely to the greater temperature in equatorial regions. So that layer of the atmosphere, at least, is nearly twice as thick in warm regions than it is in cold regions. See: