Sometimes I can make more money with a slightly higher price than matching the lowest price on certain routes. If you loose market share and you see that the prices of your competitors have not changed just hit the saved button and you'll gain that market share back.
You run some routes on losses and make up it in the others so that you can take out the smaller airline early before they get a chance to grow big. So they pull out of the route
You don't ever have to run a line at a loss. I adjust the price until my airline makes money. Sometime I match the lowest price, other times I can charge a high price and make more money than matching the lowest price.
R0 World just reset while I was playing at 20:46 Pacific time. I started Accord airways in the middle of 1950 and finished #26 overall and was one of the top airlines in reputation. While this world is difficult, you can do well and even compete against spammers.