I made sausage and corn chowder the other day. I added both corn starch and Knorr's instant leek soup as thickeners. It simmered over the stove for 25 mins. I thought it may have been too thick, but I resisted the urge to add any more liquids. I let it cool, then took it to work to share. It was reheated in a crockpot at low for several hours and became very soupy or watery. What happened to my chowder?
Unfortunately, cornstarch does that. It does not reheat well. Potato starch is even worse, and that's the thickener in Knorr's Leek Soup.
If you want to reheat something thickened, your best bet is to thicken it with a roux. There are other more modern thickeners (think molecular gastronomy), but I don't know much about those.
Attention - possible gross information to follow. Queasy fellows stop reading here, please!
Long simmering aside: If some saliva has gotten into your soup (e.g. someone tasting and double-dipping), corn and potatoe starch might break down, too. This is caused by an enzyme (Amylase), that breaks the loger starch down into smaller particles. (see Wikipedia: Amylase) The enzyme stays active; it's not "used up" after splitting some starch, therefore a very small amount of saliva can liquify an entire pot.