You should remove only the oil with a cotton swab before applying eyeliner for it to last longer.

My eyeliner looks fine in the morning, but by the afternoon, the outer corners of my eyes would fade, which was actually kind of stressful.
Especially on days when the outer corners of my eyes smudge and I look like a panda, I find that redrawing to fix it just makes it look messier.

So these days, when I do my makeup, I only do the outer corners of my eyes a little differently.

Before applying eyeliner, gently roll a cotton swab around the outer corner of your eye once or twice to remove excess oil, and lightly dab on a very small amount of powder.
Next, instead of drawing a thick eyeliner line all at once, I am drawing it thinly.

The important thing is not to draw over it immediately just because it has smudged.
I found that I had to wipe away the smudged parts with a cotton swab first to remove excess oil, and then redraw it to get a clean finish.

If you, like me, find that makeup smudges particularly easily only at the outer corners of your eyes, try controlling the oil around your eyes first before switching products.
The staying power is quite a bit different than I expected.