If the military instants of which you speak are the ones that add regiments and battalions, they only add to the troops you have available. They do not effect the fighting except for making more troops available in the pool from which you draw your troops. So if you are facing 10,000 of the enemy and you have 8,000 of your troops you can use, adding an instant won't raise the 8,000.
On the other hand, if the military instants of which you speak are the ELR (Enlightened Light Range) or MMM (Magical Mage Multiplier?), they only effect those particular troops so if you don't use them in the fight they will have no effect. Even when you use them though, the number of troops you are using will not reflect this, though the battle will.
If you are losing consistently there may be other factors. Note the squad sizes and see if you are in a reasonable range to have a chance. If the squad size you are using is only 80% of the enemy squad size auto-fighting might not work without some other things -- like the right military instant, a Dwarven Armorer, feeding the Fire Phoenix or adding a UUU (which stands for something I don't remember, but which adds 25% more protection to all your troops, like the Dwarven Armorer).
Finally, even if you have "all the right stuff" in place you can still lose due to a really bad layout of the fighting arena. Sadly, you can't see the arena in which you will be fighting unless you actually do a manual fight. Auto-fighting is just taking a chance which, most of the time is fine, but which will generally use more troops.
Hopefully, this helps explains some of the problems with fighting in general.
AJ