Can e.g. SATRIX or Easy Equities go the same way as ZAR X recently? If it goes south, do my investments survive?
Any business that needs a licence to operate can go that way if they fail to live up to the requirements, or run out of operating funds, or whatever.
In SA, you own the underlying shares. If Satrix go out of business, their assets will most likely be bought by another company, and you'll continue as normal. If you are invested in their funds, probably the same, but if the worst happens and their funds have to be disbanded, there will be some (no doubt, drawn out) process to recover the underlying shares and parcel them out appropriately.
If you invest with an overseas broker, you may have that protection in theory, but it will be a lot more complicated (and costly, to you) to recover your investment. To this end, if you want to use an overseas broker, and/or overseas funds - stick to Europe. Consumer protections are better, tax implications are better due to the double tax agreements. Vanguard, for example, domicile their funds in Ireland. Their S&P500 (VOO) equivalent is VUSA (in GBP) or VUSD (in USD) (same fund, there's another code for EUR too) and it's traded on most of the major exchanges in Europe, so you have quite a lot of choice. It's exactly the same underlying assets, so you get exactly the same gains. The fund fees are generally a tiny bit more, but usually the tax benefits more than makes up for that.