My saltines keep just fine if I . . . (more)
Open the sleeve only as far as I need to get crackers out and then I re-seal the sleeve twisted tight shut and then put a wire twist on to keep closed. If I am feeling really fussy I will then place the sleeve in a zip lock bag, squeeze the air out and seal.
I HATE stale saltines, and the above works for me.
I have noticed that saltines of ANY brand taste better if they have some brown on them, and they seem to keep fresher longer, again if they have some brown on them. Toasted on a saltine is better.
I also have some old Saltine Cans with push-on lids and everything gets stored in there, open or closed. But the saltines wrapped as above seem to keep fine for me even when not stored in a can.
Is is very humid where you live? You might want to heat the open sleeve in a VERY low oven briefly (like just a couple of minutes, just till barely warm) and then twist, tie-off and store in a zip lock bag. Moisture in saltines, baaaaad!