I understand certain factors like how the Sack of Rome in the 390s BC caused much of Rome's founding history to be lost, but how do civilizations gradually forget things that are or were integral to their existence?
For example the overall lacking of information of the reigns of Trajan, Hadrian and Antonines Pious. Or the foundation stories of numerous civilizations, Britain and Rome in particular come to mind.
I know history has not always been as peaceful or as focused on information as we are today, but how has so much information simply been lost to time?
It's simple really: No one writes it down or those records are destroyed.
Strictly speaking, History begins with written records. Pre-History literally is defined by the lack of records. Skim through history and you'll find a litany of records we have of burned libraries but no copies of what was in those libraries. Years, possibly centuries of knowledge lost, including records that would be priceless today.
My field, Tibetology, is notorious for having a lot of missing information. Paper was very expensive, and so there weren't a lot of things like personal journals which would be priceless today. So a lot of information we would infer about, say, the lives of 12th Century nomads in Kongpo or Ngari is inferred from the lives of nomads today, of what glimpses we get from the records of settled peoples. Tibetan Buddhist authors were mainly monks living sedentary lives focusing on religion, ritual, and philosophy. We have a few histories (The Testament of Ba, The Old Tibetan Annals, The Blue Annals, The Song of the Queen of Spring, etc.) but they're few and far between, and filled mostly with great deeds, religious language, building of fortresses, the births and deaths of kings, and wars. Not really the daily lives of peoples, which is really where a lot of the information about history actually comes from.
Speaking of nomads, think of the cost of writing down history: you need a sedentary, literate society with a complex enough economy to support the production of written records (and its material culture) along with a surplus food to support scribes and writers. That seems like nothing to us in the age of the internet, but for a lots of societies (say, societies with relatively simple economies based on moving place to place, where carrying a library seems like an unnecessary waste of energy and resources) throughout history, that's a tall order.
I daresay that one of the reasons The Diary of Anne Frank is so famous is because it's the record of perhaps the lowliest member of a society. What I wouldn't give to have a journal of a Tibetan Zap in the 17th Century...