Reddit mentions of Sofix Stone Floor Cleaner 1 Liter

What part of the country are you in? That looks like it might be bluestone, in which case it is unlikely the stone is deteriorating. I have a bluestone random flag natural stone set in concrete (it looks very similar to yours) throughout my house and it is tough as nails. In fact at one point someone jackhammered a portion of the floor (probably to get at the floor heating system beneath),and the only way you can tell is that the concrete is a slightly different color and a bit rougher. It looks like they lifted the stone out unsplit and just laid it back down in the new concrete bed.

I don't think you need to seal it for protection though the slight shine is attractive - but it seems to wear off quickly. There was some sort of sealant on the floors when we bought our house, but it didn't even last the year and the floors look great without it. I did contact a bluestone supplier and asked about sealing my floor because i thought it might be necessary, and they said they had never heard of doing that to natural stone, which surprised me frankly, but honestly, in the 10 years I've owned the house it has never seemed like something that was necessary.

As to cleaning, I used to use a fantasitic product called Sofix which cleaned and gave a slight shine. https://www.amazon.com/Sofix-Stone-Floor-Cleaner-Liter/dp/B000ASSBY4 The liquid was blue and using it to clean really played up the color of the stone (and didn't seem to harm the concrete). However, as you can see from the link, it is unavailable and has been for the last 6 months. I keep checking Amazon every few months to see if it will reappear, but no luck yet. I have not found anything comparable unfortunately. Everything else I've tried either wants you to mix the cleaner with water (which seems to just turn everyday dirt into mud), or dries tacky, or smells like a caustic chemical factory, or stains the concrete slightly. Or all of the above. Right now I'm hoarding the few bottles I have left and just spot clean the floors when necessary with dish detergent and as little water as possible.

Some of my stones also seem to have an odd pattern and in one spot looks like a deer walked across it and sunk in to the stone a couple of inches! I think it is just natural variation from splitting the stone and removing occlusions of different material from the slab.