The embouchure and body endurance of a horn player are  directly proportional to the quantity of energy available and tthe way of playing. It a process that can be compared to a car… 

How to drive longer distances faster and increase your fuel economy at the same time?  

 

As we play longer phrases or while going to the high register, even more endurance is required. 

Usually my first approach consists on using the largest amount of air (fuel) possible. Even if at the beginning it means extra breathing to allow us to reach our goals. In a second approach, we should “tunthe engine, in order to increase its power output, economy and durability. In short to spend less fuel while doing the same track, which in musical terms means achieving the same musical goals using less air (fuel).  

When we play music composed by Johannes Brahms (1833-1897), Gustav Mahler (1860-1911) or  Richard Strauss (1864 -1949) the endurance issue increases due to the wring style of these composers. 

For working German and Austrian composers’, I advice the practice of the slow etudes by Oscar Franz (1843-1886), starting on page 61 with the following etudes no.: 2-59-1119-2226 and 28-29 of the book Grosstheoretisch-practische Waldhorn-Schule. Later it is good to go on with his concertant etudes, starting on the 86th page of the same book. 

Practicing every day each etude after a nice warm up, staring without repeats on a low transposition, raising half step each day until F, following this pattern: 

(we will skip on purpose the devils’ transposition...) 

MON 
Transposing in low B flat  
TUE 
Transposing in C 
WED 
Transposing in D flat 
THU 
Transposing in D 
FRI 
Transposing in E flat 
SAT 
Transposing in E 
SUN 
in F! 

Without rush! 

Later on, when you play these etudes with the repeats it’s important to simply "survive" at first, playing from the beginning to the end and clearly thinking where to relax your embouchure, in order to save energy to the etude's climax, even if that means  reducing the dynamic amplitude. Then you can gradually start playing all the written dynamics, and if you want to take it no the next level, you might want to try playing each etude twice with repeats, without stopping.

For tracking your evolution, take a note writing down the date and on which bar do you start to feel tired, and which bars did your embouchure collapsed. Then compare your evolutions after a few weeks... by then you might still not be totally satisfied with your playing, but looking back and seeing where you´ve been and where you are, helps reestablishing our goals and refill with energy.

It is important to consider two different types of enduranceshort term and long term endurance. 

Short term endurance depends on the energy your body can spend on a  difficult but short passage. Long term endurance depends on the resilience (the ability to properly recover) of your body  and the energy management during a concert. Both depend on the daily practice, but can benefit also from critical planning: where to rest (play with less energy) and where to spend more energy.  

The plan I present in my website How to improve your embouchures' endurance? can also be very usefulsince sometimes lack of endurance has to do with lack of energy managemenand overplaying. 

The pedagogical importance of Oscar Franz etudes goes further than endurance practicing as they are excellent for practing music phrase leading and sound control. 

What you practice and how you practice might help you to improve your endurance, but you can adopt this gold rule:
No horn player can have endurance without regular practice!