If metal gets "softer and easier" with bending back and forth, it is because micro cracks are forming in the metal. These cracks reduce the amount of metal resisting the bending, so it could get "easier" to bend. But of course, the cracks weaken the metal, leading to failure, obviously not something you want with a nib.
Most metals don't get "softer and easier" with bending, though. As the metal bends, atoms of the metal slide over one another. When the metal is allowed to spring back to it's original position, the line of atoms slides back to it's original site...if it can. All metals have crystalline defects: the neat line of atoms has been disrupted by impurities, alloys (different sized atoms), or just missing atoms (entropy at work during cooling and crystallization when the metal is poured at the foundry). When a nice line of atoms sliding along meets a crystalline defect, the line stops sliding, and may get snared by the defect. With repeated "extreme" bending, more and more lines of atoms get snared, and can no longer slide freely. Thus, for most metals, repeated flexing past a "certain point" causes the metal to become brittle (most lines of atoms are snared and unable to slide). Enough snares, and the metal breaks. Just before the break, the metal seems to bend easier, but that's because it's already started cracking.
Metal such as steel can be bent zillions of times if the bend does not go past that "certain point" (the elastic limit). As long as your steel flex nib is not flexed too far, you are safe. Non-ferrous metals, such as gold and copper, have lower limits, so these nibs should be treated with more care. Micro-cracks are common in vintage gold nibs, according to some pen repairmen. I think some micro cracking of gold can be repaired, but I'm not a repairman.
Unfortunately, I can't give you a good handle on the "certain point." This is something that I learned by feel while working with metals, and I suspect most pen users learn similarly. A key nib symptom for "bending too far" is when the nib tines won't return to their normal position. This problem usually can be repaired a few times, but further bends past the elastic limit will eventually weaken the metal so that the nib fails, alas.
Hope this helps.
Nice article comparing gold and steel for nibs:
For information on metal fatigue:
Edited by Brooks MT, 18 February 2014 - 04:47.