Mono does have a shelf life (not sure exactly how long as it depends on storage), in my experience the good brands are fine for a couple of seasons anyway if kept in a dark place and out of sunlight. Store in a cool place during the off season.
Since you are having problems with mono to mono connections and just not with fluoro to mono here are a few thoughts and questions to consider.
3X is pretty strong and in my experience more than strong enough for most trout fishing. Are you fishing for trout? I seldom ever need anything over 4X.
How tight are you cinching down your knots when tying them? You need only to snug the knot down with a steady gentle pull working it tight by pulling on standing and tag ends. Do not snap a knot tight as that will greatly weaken it!
To see if you are snugging your knots down properly look at one after you have tied it by viewing it through a pair of binoculars looking through the the binos in reverse. Any knot you tie should look fairly even and all wraps snugged down. Compare how the knot looks to a good diagram.
I prefer a double surgeon's knot, 4 passes through. Try 4 passes through instead of 3.
Could you be setting the hook to hard when you get a take? I have a friend who over reacts when he gets a take and sets the hook violently when he strikes back. He often experiences breaks offs, but usually when he strikes back. It could however weaken a knot causing failure later in the fight.
Hope you get it figured out. Confidence in ones knots is paramount to good success especially if you target and want to land big fish consistently.