swords will break. Weapons will run out of ammo, or at least need to be reloaded. If you are facing one hundred thousand zombies (just one heavily populated city, of which this country has several) then killing an average of one zombie per second for 24 straight hours, you will still have almost fifteen thousands zed-heads coming after you. Even the most highly-trained soldiers on earth would be hard-pressed to spend twenty four consecutive hours in combat without respite.
In a true zombie *apocalypse* situation, the only realistic response which might succeed is either a well-prepared, well-executed offensive sweep. Any attempt at defense and the bodies will eventually pile too high for you to get clear shots, and therefore you have to wait until the "live" Z's are over the wall. Rinse and repeat that a few times, and the wall gets closer to your position until you're overwhelmed. Fall-back strategies could mitigate this, but success ultimately relies on you having enough retreating space, and a way to keep that space clear.
A properly executed sweep would sequentially create fresh territory for the dead bodies to be piled in. Regular clean-ups would follow in the wake, and defensive checkpoints would periodically be left behind to monitor other points of entry. Perform the sweep along the coastline, so that expedient naval retreat is always an option. Don't try to hold ground, because only complete annihilation of the enemy to every last man will win the day. Simply perform the sweep, pull back to the ships, bait a fresh batch of Zack, and sweep it again. A temporary off-shore agricultural ecosystem and wartime economy must be maintained until enemy numbers are depleted enough to begin holding the mainland.