Is that actually what happens? I'm trying to picture the shake surviving in your stomach acid before passing along the intestinal tract for the nutrients to be absorbed and I'm pretty sure that can take more than 15 minutes and there have been plenty of times where I've left a shake sitting for half an hour drank it and been fine with no untoward effects on myself or rate of loss. Not saying you are wrong just never heard that reason before.
What definitely does happen though if you leave it sitting is that the iron* in it forms a sediment at the bottom of your mug which for women I can see being a potential cause of developing symptoms of anaemia if you're not getting the full iron benefit from the shakes and you're TOTM rolls around.
*In case anyone is wondering, back at school we did an experiment with mushed up frosties a small magnet and something to spin the magnet inside a beaker to keep agitating the water/frosties solution. The magnet came out covered in a fine black crust, iron.