I’ve had this experience a number of times.
Last one was the dream before waking this morning. I was sat at a round table and was so tired that I rested my head on the table top and felt like I could nod off to sleep.
I’m guessing it is due to not getting enough hours sleep / getting up daily at a time not suited to my personal body clock.
Same here, experienced this many times. This is sort of unrelated, but I wanted to wake up from a dream last week and wasn’t able to. I decided that I had to fall asleep in the dream to do it. I was right, or it worked at least. Weird that I wasn’t lucid during it 
This sounds familiar to me too, but I have had it more often in lucid dreams. Maybe I have just been more conscious of it then?
I have extensive experience with this. Essentially I suffered an extremely traumatic event that really screwed me up mentally for a couple of years but also fortunately forced me to adapt extremely good meditation habits. I only recently (literally like a month or two before I came back to ld4all) got over it. I was never quite sure what caused it, but basically for two years straight all my dreams involved me being tired in my dreams. My recall was piss poor and my number of spontaneous lucid dream plummeted from like a one a month to 0. According to doctors, the type of trauma I suffered causes a good 6 months to year of fatigue, which would have been fine except for I couldn’t sleep a full 7-8 hours. The problem literally went away as soon as my sleep had definitely improved so yes I think that is a huge factor. I do want to mention, even after my sleep improved I did have to work on my mental alertness a bit too to get my dreams back (in a manner of speaking). But I believe the latter was more a result of the trauma and not related to your situation since you are an avid dreamer 
This is a consistent dream sign for me. So many times in dreams I am trying to sleep, or looking for a place to sleep, or getting disturbed while trying to sleep. I always thought it was related to my insomnia issues from being on call in the middle of the night. -Some kind of anxiety related to having my sleep disturbed so often, that even when asleep I dream that I am not getting good sleep.
Tried using it as a trigger for lucidity, doing reality checks whenever I felt tired, but since that was a constant occurrence, never got it to work. 
i also very frequently dream of sleeping, being tired and having to go to sleep in random places (often public places or weird places to be sleeping), or lucid dreams where all i want to do is sleep.
i find it strange that ive never read about this phenomenon in any books or studies on dreaming or lucid dreaming, and ive read a lot. does anyone know of any references in the literature?