The only way the frame can become less stiff is if there is a crack (or a number of micro-cracks, or some heavy corrosion) that has an effect on the overall cross sectional area (and therefore stiffness) of the frame.
If it’s feeling flexy, I would check the whole frame very carefully for cracks.
Not a frame builder, but I deal with rusty/cracking steel every day at work, and have felt cracks on a couple of steel frames before finding them – one on the down tube, so could’ve been quite nasty. And neither were on any of the main frame welds (the down tube one was on a shifter mount, the other was away from all welds on a chainstay).
I can’t see the micro crack scenario being that likely, but maybe corrosion or more likely a significant crack can happen.