This is indeed annoying and the solution to it is simple: waking up with an alarm.
An alarm wakes one up with a start allowing to concentrate on last thoughts, where as upon emerging from a dream without an alarm or any sudden awakening the memories fade while one isn't fully aware yet.

However, as I've experienced lately for some reasons, it's possible to wake up before the alarm goes off sometimes, waking up naturally and forgetting dream memories.
Just woke up at 6:30 AM today when my alarm was set to 7 and forgot just about everything except for a dream I had at the beginning of the night and recalled only because I had awoken after that REM period. All other dreams faded due to natural awakening, surely annoying, heh.