+1,
Usually this is a sign of wear or damage. The FD isn't designed to keep chains on rings, only to shift them at low tension. You might also be having similar issues on other rings, but the bigger ringer acts as a catcher.

Id start by taking the FD out of the equation altogether by removing if the cage can be opened (some can, some can't), or if you have a reusable connector on the chain. The bike should ride fine as a 1x? with the FD. Now maybe you can observe what's happening, and maybe see the problem.

Just to eliminate it as a possibility, shift the rear to about the 3rd in, and sight down the chin like a rifle. It should be very close to straight, on the 3rd or 4th rear sprocket and outer chainring. If the cassette is noticeably outside of the chainring, that may be a factor, but I'm hoping that you don't have this issue.

If you can't eyeball an obvious cause, here's things to look consider.

If it seems to happen at the same place on the chainring each time (foot position is the same) then it's the chainring.

If it happens randomly, it might be the chain.
If it only happens under load, it's chain or chainring wear (or both), measure the chain for stretch, which should be below 1% (1/8" over 12"), co check by using a screwdriver blade to lift the chain away from the chainring at the 1/2 wrapped position (front of bike). You shouldn't be able to lift it away enough to see more tan 3/16" of daylight between the chain and sprocket. If you can, what may be happening is the high tension shifts the chain back on the sprocket, so the next tooth coming to engage bumps a roller instead of falling into the gap. That lifts the chain, and allows it to climb over the side.