Right at the beginning of the Tur and Shulchan Aruch, siman 1, it says that it is better to pray a little with kavannah (proper concentration?) than more without. I don't know that anyone argues. I also don't see it put into practice in many places where I might have applied it.
The Rambam (Hil. Tefillah 4(14)) says pretty clearly that we should not daven at all without kavannah, and if we did, go back and pray again. But, later authorities seem to tone it down - after all, we don't have so much kavannah anyhow.
That is pretty much the answer I have gotten when I asked, say: I'm really tired. Maybe I should sleep instead of going to shul for maariv, and hope I get up in time to daven later. No, no! Go to shul now and do the best you can.
Maybe I should say less of Pesukei D'zimrah? No, no! Birkas Krias Shema - are you nuts?
Anyhow, when Slichos comes around I really struggle. Do I have more kavannah, or am I just stretching the kavannah I have much thinner? By the time I get to Hodu I'm frequently exhausted [I do have health issues with fatigue]. What should one do? "How can you think of skipping prayers at a critical time like the Aseres Yemei Teshuvah?!"
I'm asking for sources for practical rulings, but also advice on the right attitude.

Update: On re-reading, I don't want the impression that the question is based on my physical situation, as if I'm tired all the time. The real question is more based on a mental weariness, on one's ability to "hold kop", the point where one feels prayers turning into mechanical reading without really paying attention.