I remember reading it online about 10 years ago, someone linked the story. There were two sides fighting, one from the future and one from the past, and instead of fighting for land they were fighting for time. The faction from the future was winning because they had better tech, and the line of skirmish kept being pushed further into the past. The past faction knew they would lose, but it was like the theme of the story that you have to fight anyway.
Sounds like somethng Ballard would write, but I don't recognise it.– Daniel RosemanSep 19, 2018 at 14:32
Hmmm, I perused Ballard's short stories anthology and didn't find it. I did the same with Asimov. Do you happen to know other sci-fi short writers that might write something along those lines? ...I really want to find this story.– Jared SanfordSep 20, 2018 at 4:08
2Were the factions called "spiders and snakes"?– Emsley WyattSep 21, 2018 at 4:27
I'm afraid not, different story but thank you for trying.– Jared SanfordSep 21, 2018 at 6:09
Perhaps Michael Swanwick's "Legions in Time"?
There were two sides fighting, one from the future and one from the past, and instead of fighting for land they were fighting for time. The faction from the future was winning because they had better tech, and the line of skirmish kept being pushed further into the past.
"Hero mercenaries," she said, "I salute you! As you already know, we are at the very front lines of the War. The Aftermen Empire has been slowly, inexorably moving backward into their past, our present, a year at time. So far, the Optimized Rationality of True Men has lost five thousand three hundred and fourteen years to their onslaught." Her eyes blazed. "That advance ends here! That advance ends now! We have lost so far because, living down-time from the Aftermen, we cannot obtain a technological superiority to them. Every weapon we invent passes effortlessly into their hands.
"So we are going to fight and defeat them, not with technology but with the one quality that, not being human, they lack–human character! Our researches into the far past have shown that superior technology can be defeated by raw courage and sheer numbers. One man with a sunstroker can be overwhelmed by savages equipped with nothing more than neutron bombs–if there are enough of them, and they don’t mind dying! An army with energy guns can be destroyed by rocks and sticks and determination.
Formerly online at the Asimov's website and now available at the webarchive https://web.archive.org/web/20041208165439/http://www.asimovs.com/_issue_0406/legionsintime.shtml
Could be "Palimpsest" by Charles Stross maybe?
It was available online for a while in 2010 (roughly the correct time from the question): http://www.antipope.org/charlie/blog-static/palimpsest-intro.html
The wikipedia synopsis is quite brief ( https://en.wikipedia.org/wiki/Palimpsest_(novella) ):
Pierce is a police officer with the Stasis, a special institution dedicated to the preservation of humanity by its agents who are able to travel through time. After every extinction event resulting in humanity's end, the Stasis reseeds Earth with a replacement group of humans time-jumped from an earlier era. However, the Opposition, an organisation that seems to struggle against the Stasis, has been created over time, and it seems that Pierce is somehow tied to it.
My personal recollection (I've not read it for a while) is that the events in this story are more "cold war" style skirmishes whereas the question hints perhaps that it was more "open warfare".
One key theme was that there were quanta of time and each could only be travelled to once. i.e. if a group needed to go somewhere, each person would permanently use up one of the quanta. Although they were dense, there were significant parts of the timeline that were getting "used up" around key events so were getting difficult to modify/counter-modify. This does fit in with the idea of the confrontation being pushed back in time as they have to give up on one event and attempt to modify an earlier one.
I think this was the same story where your "graduation" into the Stasis involved "cutting you out of time" by you yourself jumping back a fraction, appearing behind yourself and killing yourself.
Finally, I had not realised this, but it was loosely based on Asimov's story "The End of Eternity".