Yeah, you can have memories that are totally beyond recollection. Think of it this way:

For a memory to be intentionally recalled the part of the brain responsible for intentional recall has to be 'wired' to the memory. When you're very young this region isn't sufficiently developed, so you can't intentionally recall things from when you're a baby (most people that is).

It can happen with severe fear responses too: there's a neural pathway proceeding from the amygdala through the hypothalamus and into the prefrontal cortex. When you have a powerful fear response the hypothalamus inhibits the signal to the prefrontal cortex, so no information reaches that area and it gets 'left out of the loop' so to speak. I may be wrong, but I'm pretty sure the prefrontal cortex plays a role in intentional memory (explicit memory), so if it's not in the loop when the memory gets laid down it won't be 'wired' such that it can recall it.

In both cases the best (or worst) you can hope for is that the memories 'piggy back' in via subconscious association. But your mind doesn't want to experience the pain; the best way to avoid it is to avoid what caused it, so your brain retroactively associates the pain with those thoughts that preceded it. This allows trauma-sprawl throughout your neural networks and leads to general memory loss over time because the associative web capable of triggering the trauma is always growing and annexing otherwise harmless associations.