And that is the point why I think Ardor won't take of as a Blockchain-as-a-Service Platform:
What happens when a child chain gets pruned? Can the child chain creator choose when pruning happens?
For instance:
If I have a company with supply chain, that wants to put information onto the blockchain. What happens when a supply takes... lets say 6 Weeks, due to shipping or something else but the chain gets pruned every 2 weeks?
Are the information lost? What happens in case of a warranty and I need the information on the blockchain?
The last state of a node (e.g. its last balance) is not deleted by pruning - it's recorded in the account table (snapshot).
So if a company is afraid to lose information they could - apart from running archival nodes, as martismartis said - simply create a new account for each essential transaction that shouldn't get lost.
However, I don't believe that the scenario you describe is really the ideal use case for an Ardor childchain. Ardor childchains are best used when the last state of each account is the important information you need, not for the "data storage (with timestamps) in the blockchain" use case. Use cases would include internal payment networks (e.g. bonus point or gift card systems), in-game currencies (e.g. Linden Dollars) etc.