Endurance

en·dur·ance
1. the ability or strength to continue or last, esp. despite fatigue, stress, or other adverse conditions; stamina:
2. the fact or power of enduring or bearing pain, etc. 
3. lasting quality; duration

Lets look at some published Longer Duration methods incorporating the kettlebell that we can use to train for improved endurance.

Intervals
A very good example of an endurance kettlebell interval is that of the “Viking Warrior Conditioning”(VWC) Protocol. There are a couple of specific interval options in this protocol, but Ill focus on the :15/:15.
The protocol specifies performing a Kettlebell Snatch as follows :15 Left/ :15 Off/ :15 Right/ :15 Off. That format is repeated for the desired time with the protocol topping out at 40:00 of duration. Also prescribed is a rep count of 8 reps per interval. Obviously, these intervals can be worked for less duration and for less reps per interval.
If performed to the “Maximum” with a moderate weight...we will say 16kg...we would have:
40:00 of Total Time
640 Reps
10,240kg (22,575lbs)
Not a bad use of your time in my opinion.

Kettlebell Fitness Protocol
The World Kettlebell Club (WKC) Fitness Protocol is another good utilization of the kettlebells for endurance efforts. The protocol is very much assimilated to sporting efforts, where there is a “one time” hand switch during the working intervals. The Fitness Protocol runs a progression of work/rest intervals ultimately delivering the user to the Level 20 which is:
3:00 Left/ 3:00 Right with a :30 Rest between intervals. At maximum, this interval is repeated 6 times in succession. For easy comparison I'll once again use the snatch at what is prescribed for max of 24 RPM and using a kettlebell weight of 16kg.
39:00 of Total Time
864 Reps
13,824kg (30,476lbs)
Again...A pretty good use of training time.

Having done each of these protocols at various times over my kettlebelling career, I can speak first hand as to the physiological effects that they had on my body.

The VWC was a challenge for me as the speed of execution of the snatch plays a fairly big roll in the in attaining the max rep numbers prescribed. Heart Rate elevated and stayed an average of about 155 BPM for the duration. Although on the face of it with the intervals you are resting for half of the actual session it feels nothing like rest.

The WKC Fitness Protocol was a bit more of a challenge for me from a “one arm” endurance standpoint. There is nothing that I have found easy about performing longer sets with a one time hand switch. Not only do you have to focus on a pretty good speed to maintain max RPMs, you also have to impart a good bit of “intestinal fortitude” and discipline to endure (that is the appropriate word) the long sets with that one time switch. Heart Rate again stayed elevated at about 155 BPM average for the duration.

These are just a couple of the endless training options you can use for endurance training with a kettlebell.

Either way you slice it there will not be too many intelligent people that can argue that holding a 155 BPM HR will not have a positive effect either increasing or sustaining ones endurance. As if it needed further support, Ill offer this excerpt from the American College of Sports Medicine:
...our study instead focused on the heart rate, oxygen consumption and caloric expenditure responses to a typical kettlebell workout. We found that HR and VO2 values were easily within ACSM guidelines for providing an aerobic training effect, and the number of calories burned was similar to jogging at 6 miles per hour or biking at 15 miles per hour. This is unusual for an activity that is viewed primarily as a weight training regimen.

The above excerpt sums up WHY a kettlebell is a very effective Endurance tool. If you desire a greater detail of the bio energetics and more on specific energy systems run yourself a Google search. That will give a much better explanation than I can give.