Sounds to me (assuming you have used more than one lock ring with the same results) that the threads of the hub have somehow been enlarged. I would consider using some BLUE Loctite on the the ring threads if you don't want to replace the hub. Make sure the lockring you are using has good clean square teeth and isn't a worn one. That would make it very difficult to remove.

Yan can change the freehub only. That's where the problem is located it seems.

Louis :)

^This. Call Hed.

Are you sure you’re getting the 11t seated properly? I’ve never had a cassette loosen in 35 years

I'm thinking...., what do you mean by : -" I converted...." ?
Some 11 speed conversions are sketchy...you may have damaged the threads, or the person may not have machined the freehub splines ( or the bigger cogs body) deep enough to allow the lockring to get a decent grip.
Have it checked by somebody competent.

Louis :)

I simply bought one of those - https://store.hedcycling.com/11-speed-conversion/

The install was done at the local Helen's cycles....

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Next races on the schedule: none at the moment

Well. Like discussed earlier, my first impression is it should be the threads that are too wide. You might have to change the freehub, and use a new lockring, prefferably steel. Light alloy freehubs and lockrings aren't very sturdy.

Louis :-)

Do you think that simply putting some loctite on would do the trick?

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Next races on the schedule: none at the moment

You can try that, it won't cost anything but the Loctite and it's not dangerous.
I would double up with a new steel lockring for better bond.
You sure there are no spacers between the cassette and freehub? You don't need any.
If it holds on for a long period, then fine. Don't try this before an event though...

Louis :)

Especially the lock rings. Can't tell you how many Dura Ace, Super Record and Record lock rings I've had failover the years...

Yep, doublechecked that I had no spacers, etc. Will try the loctite today. Thankfully it's just my roadbike, so worst case scenario it's an uber ride home....

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Next races on the schedule: none at the moment

Try putting a little grease on the freehub body itself before installing the cassette. It could be that the cassette isn’t seating entirely when you install the lockring, and then when you start riding it would work itself down and the lockring would lose all of its preload.

 
Assuming you've tried different cassettes with different lock rings, then it appears that the free hub body is the issue, so I'd look at what it would take to resolve that issue first, rather than

If Loctite doesn't work I'd try to get in touch with HED to see if they'd warranty the freehub body....seems like it might be defective (assuming you bought it new from an authorized retailer). Although I did once buy a like new never used HED 11 speed hub conversion kit on eBay once that the pawls or something was sticking really bad as it wouldn't coast very well at all (even just holding the wheel by the axles by hand it felt like the brake pads were dragging...even though at the time it wasn't nowhere near the wheel at the time). I got in cotact with HED then sent it in directly to them and they couldn't find anything wrong but the guy I worked with sent me a brand new one instead for all the trouble (all I had to do was pay for shipping both the destination/return). Nice customer service gesture of them actually.

How close is the frame to the lockring when the wheel is installed? There should be a small gap, ie. the frame should be pressed against the hub endcap but not the lockring. If it is, then it could be loosening off the lockring as the wheel turns. A photo (top view) of the wheel installed would be helpful to diagnose the issue.

The lock ring has teeth on its inner face that mate to grooves on the outter face of the last cog. When tightened these teath/grooves should engage and provide a "detent" to prevent the lock-ring from loosening. As such, the lock-ring should click into place several times as you tighten it down with one final "confidence inspiring <click>".

Given that you've tried this with several cassettes, I'm assuming that they all <click> into place. It would be pretty strange for all of your cassettes to not have the detents. Nevertheless, I have to ask...

Assuming your answer is "yes, they all click", I'm leaning like everyone else. It sounds like your freehub body has been stripped, or perhaps has cracked allowing it to expand under load and then the lock ring slips a thread or two...then its loose enough to just vibrate out. If the freehub body were cracked that's what you would expect to happen under high chain-tension situations.

An update. I pulled off the freehub, it looked fine, no visible cracks, etc. Called HED and they think that there is a spacer missing - it should be there. I sent them some pics and they should be getting back to me shortly, hopefully confirming the missing washer/spacer theory.

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Next races on the schedule: none at the moment