I've always fell asleep quickly until my last job became stressful (in a bad way, not the useful type) and then I became unable to sleep for days at a time. It was killing me.
What helped me cure the problem was understanding it, which I managed by reading "The Promise of Sleep" by William C. Dement. It explained a lot of things that made no sense to me before. The basic principles aren't that complex, which makes it all the more shocking that general practitioners are terribly ignorant about sleep disorders and treat sufferers wrongly.
I totally recommend the book to anyone who has any concerns about sleep.
Key points are that there are several competing factors that determine whether you are sleepy or not. The main ones being sleep debt and the Circadian rhythm.
Sleep debt is simply the idea that for every two hours you are awake, you develop one hour's worth of sleep debt that needs to be paid back (for an average person.) The more sleep debt you have, the more sleepy you tend to be. Sleep debt is cumulative!!! If you continuously sleep less than you need, the debt gets large - and a single, long sleep session may not clear it.
The Circadian rhythm is often misunderstood. It is not what makes you sleep once a day. It is what makes you alert twice a day. Once in the morning to wake you, and again in the late afternoon to help you resist the sleep debt that you have accumulated during the day.
There are other factors like stimulation and caffeine, etc. but the above two are the main ones, once you understand them it can explain what otherwise seems like illogical effects.