Right at the beginning of the Tur and [Shulchan Aruch, siman 1][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)][2]) 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 kavannah for more, 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?!"  
Also, what if a person can follow with the words, and pays attention, but is past the point of *enjoying* what's happening? He might have felt more *inspired* if he had said less. Does that play a role?  
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.  
Update: tesvov has suggested in a number of comments that the principle stated by the Tur *only* applies to optional additions, like the Tikkun Chatzos that is the topic where he states it. Interesting suggestion - obviously Rav Avigdor Miller quoted below disagrees - and it would be good to have an explicit statement by a posek about it. [ \[Berachos 34a][3] might be a good source on this, but of course in those days prayers were more fluid.]


  [1]: https://www.sefaria.org/Shulchan_Arukh%2C_Orach_Chayim.1.4?lang=bi&with=all&lang2=en
  [2]: https://www.sefaria.org/Mishneh_Torah%2C_Prayer_and_the_Priestly_Blessing.4.15?lang=bi&with=all&lang2=en
  [3]: https://www.sefaria.org/Berakhot.34a.11?lang=bi&with=all&lang2=en