The way to keep saltine crackers fresh longer after opening the saltine crackers is to keep the saltine crackers in a sealed airtight container.
So you could put the saltine crackers in a jar with a lid on it or a plastic container with a lid and they will keep for up to a month.
Saltine crackers go stale and bad pretty quickly and beyond one month there's nothing you can do to keep saltine crackers good longer than a month.
After a month even sealed in jars or containers the saltine crackers will start to go bad and will take on a bad smell such as an ammonia smell.
So eat the crackers within a month and if they smell bad then throw them out.
Sealing saltine crackers in a jar or other plastic dish with a lid helps to keep pests and other bugs out of them as well.