There are several stories where it seems the Sontarans had not acquired the secrets of time travel (though they did invade Galiffrey in the Invasion of Time and they were interested in the time experiments of Kartz and Reimer in the Two Doctors) and (as pointed out here) one story where they do posses limited time travel capabilities. Is there any reason why (presumably) the Time Lords didn't allow them to fight in the Last Great Time War (obviously, the fewer battle fronts for the Time Lords to fight on the better for them)?
The Time Lords had a pretty proud leader: Rassilon. Keep in mind, the Time Lords were pretty desperate towards the end of the war (the Tenth Doctor listed the horrors they would revisit upon the universe if they returned). The Time Lords were messing with creation itself and Rassilon would summarily execute anyone who questioned him.
This wasn't war like the Sontarans knew. We don't see the Sontarans doing much beyond conventional battles. If the Time Lords were rewriting history wholesale, the Sontarans were out of their league. It would be like bringing Roman Legionnaires to the Battle of Yavin IV in Star Wars.
The Sontarans do not have access to the kind of spacetime travel that the Time Lords and the daleks possess. That the Time Lords possess this kind of technology goes without saying. The daleks, on the other hand, have showed different time travel capabilities at different points in the series. In "Resurrection of the Daleks," the Doctor says that they only have relatively crude time tunnel technology. On the other hand, the third dalek story, "The Chase" shows them with technology comparable to a TARDIS. So they certainly possessed the requisite time travel ability at some point in their spacetime history.
The Sontarans, while they do have some time travel capacity, as demonstrated in their first appearance in "The Time Warrior," do not have the ability to travel completely freely around space and time the way the other races do. We know this, because they tried to conquer Gallifrey in "The Invasion of Time" to get ahold of the Time Lord's TARDIS technology, with which they could conquer not just all space but all time as well.
Without this level of technology, it would presumably be impossible for the Sontarans to involve themselves in the Time War on their own initiative. Neither of the two primary parties in the Time War would be likely to try to bring the Sontarans in. The daleks would not admit the necessity of using another inferior race as a major ally, and the Time Lords had already experienced the Sontarans as dire enemies. Neither would be eager to pull Sontarans into their conflict.
In the Big Finish The War doctor series specific 3. Doctor Who: The War Doctor - Agents of Chaos, in the second of the three 3 stories on the disc called The Eternity Cage, The Sontarens did try to invade the Time War to participate in it. The Doctor more or less said that their exclusion was because fighting in the Time war, required a level of skill, that the Sontarans simply did not posses.
I guess if where to use a modern day example having the Sontarens fighting in the Time War would be like have a man with very little military training fight in a Special forces mission. They would be more of a hindrance than any real help.