The verdict is out on whether squirrels forget about half of the nuts they bury: surely some squirrels do. Forgotten nuts and acorns grow into trees, so squirrel absentmindedness produces some ecological benefits. While it’s almost certain that squirrels indeed forget some subset of the nuts that they bury over a nut-burying season, it’s not clear whether these are truly forgotten or simply abandoned in favour of food that is easier to recover.
Food storage is serious business, and squirrels don’t bury nuts randomly. They are organized, and they carry out a plan. This plan comes in one of two forms. Some squirrel species stash their food in one place, likely making the stash easier to remember, but this is risky, especially if the single cache is discovered and eaten by another animal. Some squirrel species opt for a different strategy: they bury nuts in several spots across a general area. These species appear to have developed a system to help them remember where these stashes are. It seems that squirrels are capable of "spatially chunking"—that is, placing nuts of the same type into individual caches that are separate from those belonging to another type—and this process may help the squirrels remember the locations of each cache more easily. A 2017 study involving fox squirrels and a pile of four different types of nuts showed that the squirrels were able to sort the nuts and bury them one at a time, placing nuts of one species near one another while burying nuts of another species a short distance away.
So, while squirrels might forget where they bury some of the nuts they collect, the nuts that they do remember are likely well organized.