I have never had this problem. I never even worried about this problem -- and I worry about everything.
If you google What kind of ants eat through tents, you will find that other people have had your problem, for example in Texas and Africa. There are also many hits about ants who just saunter in, rather than chewing their way in, and tips to get rid of them.
The response that sounds most practical is from Michelle Calderon, posting on the website of World Race; she used duct tape to deal with ants in Africa -- Zambia, I think. (As someone once said, if you can't solve your problem with duct tape, you aren't using enough duct tape.)
Briefly, she and her friends used duct tape to remove the ants from their tent and their ant infested belongings, and then they duct-taped the inside and the outside of the holes.
So the way the ants get in is they chew holes through your tent. I had
eight new holes in my tent courtesy of the ants. I duct taped both the
inside and outside of the tent to repair the holes.
She describes her technique in detail, with pictures.
This suggests that getting a tent made of double sided duct tape may work, but, mon dieu!