Strength most certainly does decrease. Yesterday was full-blown day one for me, and I finally dragged myself to the gym around 8 PM, after my evening class. I figured if I walked there and at least put in a little effort I'd feel better about myself and about the day.
It was my shoulder-ab-calf day, so I warmed up and started per usual. I was well-fed, pretty alert, but sluggish. Failure came early on most sets and I ended up giving up on post-workout cardio 15 minutes into it. Oh well.

I went home feeling a little better at least.
Today I'm scheduled for just cardio (which I normally would have done right upon waking, but I hit snooze one too many times), but I don't even feel like it honestly. It's an uphill battle for me personally to get to the gym that time of month. I often have to force myself, but I hate it until I walk out of there. ;-)