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During the series of Deep space 9 it has been stated that the Dominion has absolute control over their part of the Gamma quadrant. Literally this would mean that they rule every planet and race inside their borders of the Gamma quadrant via totalitarian control.

To me it sounds like the entire Dominion is at "forced peace" aside from some examples like the Teplan. The Teplan appeared in DS-9's episode "The Quickening". The people were infected by a disease in response to their resistance to the Dominion.

But then they say most Jem'Hadar die in battle and as such it was rare for them to live past fifteen years of age. How is this possible? Your entire army controls a vast region of space which is at peace, even if that peace is forced upon it. Without much resistance, battles, and wars, how does the greater part of that army still die in battle?

Considering this was true before they entered the Alpha quadrant, they had to have other enemies in the Gamma quadrant. Can we assume they were continuously under attack by neighbouring states outside of their borders?

The Dominion does not, in fact, own the entire Gamma Quadrant. Source is Ronald D. Moore, cited in memory alpha:

"The Dominion does not own the entire Gamma Quadrant. We had explored the GQ for two years before encountering the Dominion, so it's not as though the wormhole opens up in their living room. There are other races in the GQ that are not part of the Dominion and the Ferengi at least have established trade with some of them. When the Dominion told us to stay out of the GQ, it was as if China told the US to stay out of the Yellow Sea. China is the big boy in this neck of the woods, and you better take their warning seriously, but at the same time we have trading partners and allies there and hey, freedom of the seas and all that." (AOL chat, 1997)

Answering your actual question,

• 
  the Dominion does have neighbors. Considering how hostile and aggressively the Dominion treats the Alpha Quadrant, we can safely assume some violence with those neighbors.


• the Dominion faces recurring rebellious tendencies from all of its client species. Vorta occasionally betray, Jem'Hadar rebel, etc. Even if there's a .1% chance of a given planet rebelling, you're bound to have dozens of rebellions every year.


• speculation, but the Dominion probably only keeps as many Jem'Hadar as it needs right now. They can grow a large army in days, so they don't have to keep soldiers around unless they're needed. Being in constant active combat leads us to the next point...


• 
  Dominion battle tactics are straight-up suicidal. We see numerous battles with total or near-total Jem'Hadar casualties.


• Jem'Hadar never gain 'command' rank. No matter their experience, Jem'Hadar are always on the front lines, which means high casualty rates. Assuming an active-duty unit takes, on average, 10% casualties every month, a Jem'Hadar would have a 1 in ~170 million of surviving to the age of 15. A 5% monthly casualty rate would give you a 1 in ~10,000 chance of making it to 15 years old.


• 
  Jem'Hadar training is shown to be quite brutal. Speculatively, severely injured trainees are killed and a new one grown.

The Dominion was an aggressively expansionistic power, whose ultimate goal was to impose order over the galaxy by controlling whatever planets and species were possible to control and destroying those that were not. That level of expansionism necessitates constant warfare against any bordering systems not willing to submit to them peacefully. Over the course of Deep Space Nine multiple species are mentioned that had been conquered by the Dominion within the decades preceding the show, including the T-Rogorans who were conquered in 2370, and the Yaderans, whose homeworld was occupied in 2340.