Also, are there modern dishes that are headed that way but people may not realize it?
Your question is really broad, as it could apply to all of human history and it not clear how it should apply to the cuisine of different cultures.
Ingredients not existing at all would mostly apply to extinct animals. It is really hard to get a decent mammoth steak nowadays. Also any other animal of the megafauna would fall into this category. More modern extinct animals would be the passenger pigeon, which was hunted to eradication. On extinct plants only the Gros Michel banana comes to mind, but this poses another question on how much you would count the disappearance of certain breeds into your question.
Another source of unavailability would be environmental protection laws for endangered animls. Whale meat used to be common but now you can get it only in Japan or as a member of a people with traditional hunting rights.
A more common reason for disappearing food would be fashion and economic shifts. Pigeons used to be bred in all of Europe as a source of food, but today you will not find it. However, in the middle east it is still popular and you might find it on a menue of a restaurant. Modern chicken farming has left very few room for capons (castrated rooster), many people will not have heard the word. Also when is the last time you ate a mulberry? Without the need for silk production the trees are no longer common and the berries are really squishy, so nothing that would survive the modern supply chain to a supermarket.
What food will go extinct? Probably a lot of fish. Overfishing and climate change will drive many of our currently eaten fish over the edge.
ancient Roman “Posca” / Sour wine. It was a VERY common drink for mainly lower class folks in the Ancient-Classical Roman World
The recipes we have today that try to replicate it aren’t exactly 100% accurate since we don’t really have any idea on what the exact recipe for it was*(ratio of water to sour wine/vinegar, Herbs used, wine used etc)*. It also would’ve varied greatly since there doesn’t seem to be an exact Sole “recipe” for it, in some cases historians guess it literally might have just been watered down Wine that had gone sour.
Posca*(along with organized Wine production in general)* definitely saw a HUUGE decline with the end of the Western Roman Empire and it fell into relative obscurity as a common beverage
On a side note, it’s been debated that the “vinegar” a Roman soldier used to supposedly “torture” the crucified Jesus was actually a portion of that soldiers Posca ration which we he was actually using to quench Jesus’ thirst out of pity?
Silphium was an herb so popular and widely used it was put on Roman currency. But we don't know if it is extinct or we just can't identify the plant from the information we have. https://www.bbc.com/future/article/20170907-the-mystery-of-the-lost-roman-herb
There are many plants that were critical to survival of native people that are not well suited to mass production, but would have been "common" to the people foraging local to the species for most of human history. Acorns, many varieties of mushrooms, dandelions, stink weed (wormwood), etc. Not to mention heirloom varieties of grocery store produce, that while most often tastier, don't present or store as well as the ones found in grocery stores. Dandelions were so prized that their seeds were brought to the Americas by European colonists. Every part of the plant is edible.
Turtle was popular amongst the American elite until they didn't have slaves to spend all day cooking them. Over harvesting also played a role. They are mentioned in Mark Twain's list of foods he wanted at his feast when he returned home from Europe. Notably so is raccoon and the prairie chicken a bird uniquely abundant at the time because of the farming practices in the Midwest during that period.
Sea turtles have been hunted to extinction and endangerment. Now only limited native collecting of eggs is allowed in some locations.
Door mice were raised in large pots in ancient Rome as food.