In my experience after experimenting with various diets and workout routines, I've discovered that it IS possible to lose strength while exercising, however, only temporarily.
There will be a certain factor that will contribute to your weakness (lack of sleep, lack of proper nutrition etc.). Once that factor is removed, you'll naturally regain your old strength if you stick to the same program.
In other words, if you're not getting enough rest, you'll notice your lifts getting harder and harder to perform in the gym. At one point, maybe you'll have to reduce the weights altogether. But once you get enough rest (deload week or a few days completely off), you'll be as strong, if not stronger than before.
Nonetheless, it's not recommended to exercise like this (with some limiting factor), since it leads to much faster injuries and slows down progress too. It's not sustainable.
So in short, yes, it is possible to lose strength from exercises, but regaining that strength is easy (excluding injuries of course)