Can tubeless tyres just wear too thin?

I have slow pressure loss from my rear tyre. Pumped up it's fine for a ride but next morning it's lost most (but not all) of its pressure. No sign of a foreign body, no seepage of sealant and no obvious cause, I've even replaced the presta core just in case.

The tyre's done a fair few miles and given me sterling service (virtually all on tarmac); it's a semi-slick (Continental Hardpack) and the light tread has pretty much worn away. The thing is, the previous tyre exhibited exactly the same symptoms at pretty much the same stage of wear.

Since the Hardpacks can be picked up for £20 each at the moment I think I'll just replace it and save myself the angst of trying to track down what the problem is, but I was wondering whether it's possible to wear a tubeless tyre thin enough that it struggles to hold air (although the wear doesn't seem extreme and I've worn tubed tyres well beyond this).

The sealant was refreshed a few weeks back so small leaks & punctures should be sealing.