Been doing 40 push-ups a day for months and nothing has changed - what am I doing wrong?

It worked at first because it was new, and it stopped because it stopped being new. That is the whole thing, and it has a name: progressive overload, or rather the absence of it.

A muscle adapts to a demand it cannot currently meet. When you were doing 15 and pushing to 20, the demand exceeded your capacity, so you adapted. Once 40 became something you could do, the demand and your capacity matched, and there was no longer any reason for your body to change. Eight months of the same stimulus is one month of stimulus repeated eight times.

The uncomfortable implication: "40 feels about as hard as it did" is not neutral information, it is the diagnosis. If you had been progressing, the same 40 would feel easier by now. Constant difficulty at a constant workload means constant capacity.

On question 2, the number is not the problem, and this is where most advice goes wrong by telling you to do 60.

At 40 reps you are training muscular endurance, not strength or size. Those adaptations come mostly from sets that are hard within roughly 5-15 reps, taken close to failure. Adding reps pushes you further into endurance territory, so 60 a day gets you better at doing 60 a day and not much else. That is a fine goal if it is your goal. It does not sound like it is.

The honest framing: you have been doing cardio for your chest for eight months. It is not wasted, you can do 40 push-ups, which most people cannot: but it is not the thing you were expecting it to produce.

The smallest sensible change, since that is what you asked for and it does not require a programme:

Make the push-up harder so 8-12 is your limit, instead of making it longer. Options, roughly in order:

1. Elevate your feet, the higher, the harder. A chair takes most people from 40 to about 12.
2. Slow the lowering to three seconds. Same movement, far more time under tension.
3. Pause at the bottom for two seconds, which kills the bounce you have probably developed without noticing.
4. Move toward one arm: hand on a ball, then archer push-ups.

Pick one, do 3 sets of as many as you can with good form, three days a week rather than daily. Then write down the number every session. When it hits 12 across all three sets, make it harder again.

That last part is the actual mechanism. Everything else is the delivery.

One thing missing from the thread: push-ups train a fraction of your upper body and nothing at all of your back.

Eight months of pushing with no pulling is worth knowing about, both because the visible change you were hoping for depends heavily on the back, and because the shoulder does not love an imbalance that large maintained for that long.

If you want to keep this minimal, adding any rowing movement: under a table, a bar in a doorway, a resistance band on a door anchor: will do more for how you look than another twenty push-ups. Same time cost.