You could make a wood plaque, and screw the latch to that. Hopefully the plaque can get screwed into some studs behind. You could make it somewhat match the gate. Or even a board that extends from the top of the step right up to the top of the gate. Maybe with some accent piece on top (like a post cap).

add a door stop to the floor, this way that takes the full blunt of the gate instead of the latch

https://www.lowes.com/pd/National-Hardware-1-813-in-x-1-813-in-Universal-Low-rise-Stop/1000134189

Might just need longer screws. That’s a corner - that certainly has a stud, and likely two doubled up.

I don't know if this gate swings both ways but I think you should have the arm on the gate and the latch on the wall

https://www.leevalley.com/en-ca/shop/hardware/outdoor-hardware/gate-and-fence/latches/74567-ozco-gate-latch?item=01S1525

You've got the cheapest of the cheap latch set there, that's sort of sub optimal because the wee latch bar bears all of the slam when it closes.

Get something like this, a way better design that addresses all the wee one's shortcomings.

Have a metalworker make a new bar that mounts to the front wall (around that corner) and is bent to go back around the corner and then extend to where it needs to be.

Gate needs a 'slam stopper'. Someone suggested a door stop at the bottom (trip hazard) - which would stop some of the force of closing.

What you need is angle or some vertical strip that the gate arrests closure against...and the only force the latch has to deal with is the impact of the bar itself, rather than arresting the momentum of the weight of the gate (slammed, wind, or just spring/weight closure)...it's a lot of leverage that gets applied over and over.

Once you deal with stopping the gate in other ways re-securing the latch is easy enough.

Edit: other solutions are:

Soft closer for the gate. They make hydraulic and spring closers that close the gate more slowly. This can also be as simple as a string connected to the gate and the opposite side with a weight in the middle.

Depending on aesthetics it could be as simple as a chunk of wood between wall and the latch bar. You'd need to use fasteners into better attachment points - but there is likely only 1 stud in there (which you've hit with the farther 2 screws presently). This horizontal wood would help with the problem...but not really 'solve' it...as the screws are resisting the force in tension - and screws work best in sheer. You'd also need a chunk the same thickness at the gate latch to keep the gate at the same closed position.

The surfacing is likely ~3/4-5/8" thick...a better latch bar with a longer attachment plate would help - but you still have the problem with screws needing to 'grab' something. There are better fasteners - such as metal 'screw in style' drywall auger type attachments. Also butterfly clips would be good too - except that at the end of the stucco - as you already know - nothing out there to grab on to. But always if the force is applied in tension you'll just delay the problem - which is why I suggested a slam stopper. Typically this would be a 1x1-1/2 angle with the short end sticking out and the screws penetrating deep enough to embed into the stud - the longer the angle and the more screws the more the energy of the gate closing would be spread out.

If you're willing to move the gate in farther (away from camera location) you could just have a latch coming straight out the wall.

But really...as this is inside - I think using 'standard' gate hardware isn't the right solution. I'd look into other forms of 'latching'...and I suspect the goal is to keep either kids or animals out of the area...does it need latching at all?

It looks almost like you could swap the two sides of the latch. If the bar was securely attached to the wood door, then it would push into the latch each time it closed.

I have solved this at my place. Add a piece of angle iron to your gate so when the gate closes it hit the iron nice and flush, and the latch only touches just enough to close.

This is kid and wind proof.

https://imgur.com/a/g7Zt2IC

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Problem: screws don't hold because of lack of material strength screws grab onto

Solution add more material.

2 dollar solution:

1. Measure distance between outer edge of latch and wall at point where lock catches latch.

2. Remove latch from wall

3. Buy 2 ft long plank that has a thickness of step 1. Buy 10 drywall screws.

4. Horizontally attach wood to wall with screws. Allign edge of wood with edge of wall. Allign middle of plank with point at which latch catches.

5. Screw the latch onto the plank upside down.

6. Check if door closes correctly. If it does you're done. If not see 7.

7. If door don't fully close you take a knife and notch out room on the plank for the bulge of the latch to fall into. If the door closes before latch catches you need to unscrew the plank and add folded paper to the edge of the wall and screw plank back into position.

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Longer screws and also angle the screw on the corner inwards so it hits the beam.

I would switch to a different latch system and maybe add self closing hinges. Self closing hinges and hook and eye latch?

Take both parts of the latch off.

Screw a longer section of wood vertically to the wall with long screws, ideally you can get that into the stud if not use some construction glue to help.

Cut a small section of this wood the same thickness and put it on the door, under the catch, and mount the latch to the wood on the wall. Both of them are reinforced, and moved the same amount away from the wall/door

Maybe using glue, duct tape, and 100s of rubber bands?

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I dunno that's usually how I fix/make things.