I get onto the habit of practicing new rhythms almost exclusively, only to discover a loss in stamina for simple rhythms at speed.  I've noticed something similar beginners- its easier to learn and play a complex rhythm at a slower tempo (eg a 2 or 4 bar rhythm) than a simple 2/4 at speed.

I've found it most effective to build up drumming stamina with what is essentially sprint cycle training (obligatory reference to one of my favorite funny sounding words - fartlek). This means playing at speed for as long as you can, then easing up, still playing but an easier variation of the rhythm. Then playing again at tempo until you have to drop out. 

While this is like a classic runner's sprint training where you do short sprints as fast as you can, then jog it off, then do it again - I am NOT recommending you play as fast as you can for these sprints.  Even the sprinters are going for a 100, 200, or 400 meter lenghts.  I'm talking about a 15-30 minute drumming "sprint" - so you can see you don't have to be drumming fast to start to wear out from playing a complex rhythm for over half an hour.  As with running sprints (and weight lifting, for that matter) you will see a decrease in performance every time you sprint - during that session - but over the long term you gain a lot in stamina.

I first became conscious of this method when I started drumming for dancers. We were playing Brazilian Ketu rhythms with sticks. The bse for many of the 12/8 rhythm has two fast triplets (based on the typical bembé rhythm), and so you have to do these two bursts every bar. If you are not up to it, after a quarter of an hour you start to tire.  Oh, and typical dance classes last an hour and a half.

So I started dropping out.  That day the lead drummer was not my typical (Brazilian) teacher, but Alfie, an assitant to the teacher and more importantly an excellent teacher in his own right.  When he saw me fading, he gave me couple of pieces of advice, all based on the sprint idea, all of which I continue to follow.

• I could play a simpler rhythm to take a break. Even simplified rhythms can help maintain sustain the sound as well as the leads drummers task, and it's not a "failure" or cop out to play them (as earnest beginners will always feel).  In fact, it's always better to play a simpler rhythm solidly than try to keep up with a more complex rhythm.
• Adjust your position. I don't  mean your hand position which can be bad for your technique and hand health. but your seated or standing position.  Typically I lean back to stretch out my arms, as the wrists work harder the more the arms are bent.
• Consciously think of easing up on the squeeze. This is most apt for rhythms that have repeating triplets or rolls, but on any rhythm where you are struggling - try to feel where you are tense, and (in classic yoga style) bring your attention there to relax your effort.

Ultimately, it is like any practice: sprinting, drumming or.... meditating: the essential thing is to keep coming back to it.