For me it's google photos. While there are lot of great gmail alternatives these days there's still nothing like google photos unfortunately, is there?
If you are looking for a managed solution, I suggest one of those that you pay for (iCloud, Dropbox, OneDrive) since usually, paid services have at least some form of customer service and something like OP's story is less likely to happen.
[1] Also, the cloud provider where I rent the server might decide to block my account for whatever reason. To minimise the risk, I'm planning to store daily server backups on a different cloud provider.