In the long run, you would likely have metal corrosion issues. Everything eventually dissolves, at least a little, it just takes a long time. Heat and moisture "forever" is a rough environment for metal. Consider metal parts dipped in a tropical ocean for decades, or the parts inside a nuclear reactor or steam plant. This is probably why you tend to hear about pH neutral broths and such instead of perpetual lemonade or perpetual pickles.
If you heat oils long enough they'll polymerize just like putting finish on cast iron. It might take 100 years instead of 100 hours but it'll polymerize eventually. The rancid taste can be avoided by serving fast enough that the average age of the food is reasonable. In general, with good mixing and fast serving, it can't get much worse than a couple days old even if the long tail is theoretically a century old. The whole topic is a good intro to distribution curve shape.
A perspective comment: Many people do this without thinking about it. I have a tin container I've been adding dry looseleaf tea to for perhaps a quarter century. I do try to run it out completely between adding batches of newer tea, but I'm sure there's some dust in there from the last century and its been in continuous use since then. My grandma had a perpetual dry granulated sugar covered dish, and a perpetual salt shaker on the table.