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I am using 3% hydrogen peroxide for a series of operations, and the common practice is to prepare it on-site from 30% hydrogen peroxide and saline. This is time consuming and somewhat more prone to error than preparing a 3% stock. I was told this is not done because 3% hydrogen peroxide has a short shelf-life (~a week).
It may pretty well be true, and here's why. Not only hydrogen peroxide is highly unstable by itself, but its decay can be catalyzed by a wide variety of compounds. And by wide, I mean really wide; at times it seems to me that those compounds that don't catalyze it are a minority. Now, I don't know what you have in your saline, but chances are that it works on the peroxide, too.
With deionized water, this should not be a problem... or should it? See, that link by @ron says that the 30% thing is stabilized. Guess what? It means that they've put some additive into it, which somewhat slows down the decomposition. When you dilute your peroxide, the stabilizer gets diluted too, and hence can't work as well as before. This is a possible reason why you may get shorter shelf-life even when diluting with pure water.
I'm not sure what is the stabilizer they use. In any case, if you find that out, then add it during the preparation, and don't add anything that can catalyze the decay, your 3% solution should be fine (in terms of shelf-life) - but I'm afraid these additions and subtractions may stand in the way of your primary objectives.
It's difficult to tell what would happen in your particular situation, because as Ivan Neretin mentions, hydrogen peroxide decomposition is catalyzed by a huge number of substances. The easiest way to find out whether your solution is actually decomposing or not would be to test it.
Make a solution of known concentration.
If you're using an accordion bottle, cap it tightly and let it sit for a week. One liter of 3% hydrogen peroxide will contain roughly one mole of solute, and when it all has decomposed it will produce about ten liters of oxygen gas. If the bottle doesn't accordion substantially in a week's time, you know that it isn't decomposing at a rate that should concern you.
If you're not using an accordion bottle then you can cap the bottle with a balloon (or maybe even a rubber glove + rubber band) instead, assuming you've got a reasonably safe place to put the thing for a week. Again, it's going to make roughly three liters of oxygen for each 1% loss of peroxide per liter of solution, so you can just watch the balloon and wait a week. A balloon will leak somewhat, but if the rate of decomposition is significant, it will still inflate.
In general you can drastically slow the rate of decomposition by storing peroxide solutions in brown bottles and keeping them refrigerated. Unless you're using something other than sodium chloride solution or storing it in bright light in a warm room in a clear container, I'd be surprised if your solution is decomposing at a rate of more than 1% a year. However, if the concentration is important, and it sounds like it is, then a test is really the only way to know for sure.
