Do you use a high/neutral, "thumbs forward" shooting grip?
One day while I was working the range, one of our instructors was experiencing repeated feeding stoppages while shooting his new LCP with ball loads. I offered to observe him shooting it.
He's a strong young man (early 40's) with strong hands, and he favors a thumbs forward shooting grip. As he fired the LCP I noted that at least one of his thumbs was elevated and near the slide. During the snappy recoil & cycling of the LCP, his thumb (unnoticed by him) briefly rubbed against the slide. He couldn't feel it, but I could clearly see it happening. I suggested he modify his grip to lower his thumbs ... and the feeding stoppages immediately ceased. His thumb no longer rode the slide and interfered with its run and velocity.
My pair of LCP's have each fed & fired an assortment of JHP's I've used. The first 100 rounds were as reliable as those which followed. I make it a point to shoot my LCP's using a grip technique similar to what I use when shooting my 5-shot snub revolvers, though, which puts my thumb (or thumbs, when shooting 2-handed) down and away from the slide.
I've noticed that a couple of other guys, both of whom have very large hands, have been uncomfortable trying to hold and manipulate the LCP. It's hard for them to securely and comfortably hold the diminutive pistol because of the relative size of their hands.
The itty bitty pistols like the LCP don't have much slide travel/run, nor much slide mass, and it's important for the shooter not to interfere (albeit unintentionally) with the slide's freedom & speed of movement during live fire.
Naturally, not being able to be there and examine that particular LCP, observe you shoot it or try it myself, I have no way to be able to know what might be happening with your LCP.
This also presumes the LCP was inspected and found to be in normal condition before you started using it, was sufficiently lubed, and that the recoil spring/guide rod assembly is oriented and installed properly.
The use of a single magazine can't help eliminate the potential issue of a problematic magazine, either.
It's not uncommon to hear most instructors & armorers express that day in & day out, at least 95% of pistol "problems" turn out to be shooters-induced problems, than actual gun-related problems. After that comes a small percentage of ammo-related problems, lastly followed by actual gun problems.
Just some thoughts.