I actually have similar symptoms on a smaller scale - I never remember my dreams, and I generally can't tell you if an event happened in the last month or the last year.
I get plenty of sleep, though, so I'm just going to chalk that up to having a bad memory.
Obstructive sleep apnea can cause lack of REM sleep and, as a result, no dreaming. Symptoms may be such that you have a long sleep period but are prevented from deep sleep by micro-arousals. Being overweight (as Mr. Arrington mentions in a linked piece) can cause or worsen apnea.
It was my understanding (and maybe this is incorrect) that someone only remembers their dreams if they wake up during them. Therefore, not remembering them could just be a sign you've had a good, uninterrupted night's sleep. Anecdotally, this seems to be the case for me–I remember my dreams if I'm woken up e.g. by a car alarm but never if I wake up normally.
I've always been told that you have to practice remembering dreams in order to get better at it. And the often-cited way of practicing that is by keeping a dream-diary that you're suppose to write in whenever you wake up.
Likewise, I've never heard of the whole "you only remember a dream if you wake up during it". Sometimes I go through a few dreams, wake up naturally, and remember some of the previous ones (and not the last one).
I too thought this was the case. I very rarely remember what I dreamt last night, it may happen once in five months if I'm lucky. But I always thought that was perfectly normal.
I get plenty of sleep, though, so I'm just going to chalk that up to having a bad memory.