Have you checked the frequencies the competing airlines are using? And their aircraft? You also have to check your loadfactor. If they operate larger aircraft and/or more frequencies than you do, they would naturally gain more of the market as more people are flying on their airline.
A good IFS allows you to charge more money for the same amount of passengers on each flight compared to a bad IFS, as your services convince them to pay more. Also, a good IFS allows you to attract more passengers for the same amount of money compared to a lousy IFS. If you have a IFS rating higher than that of your competitors, you would be able to retain many of your passengers even when the opponents' seat prices are lower than yours. If their prices are dramatically lower than yours, they would still be able to steal your passengers from you, however. All the same, a good IFS rating would enable you to better survive a price war in the long run.
If you have a 100% loadfactor, and still have less of the market than the competition does, consider increasing the number of flights (or the size of the aircraft) to gain more passengers. You could not improve your market share even by a good IFS when your loadfactor is full because that is the limit of the number of passengers you can currently carry. Market share is determined by comparing the total number of passengers an airline is carrying on that route to the total amount of passengers being carried on the same route by all the airlines competing in it. (If you are the only airline on a certain route, you will have 100% of the market no matter how many passengers you carry or the quality of your IFS)
I hope this helps!