Good question and i guess it depends, but generally you as a service provider should always anticipate this situation and be prepared to answer to something like this. Either charge for backup from day one or provide sufficient backup as long as the client provides new work + a number of years of 'complimentary' backup.
- I always and repeatedly encourage all my clients to keep their own copy of my deliverables. Be that editable files or just straight PDF exports (when editables are not delivered).
- I will never backup files that were circulated and not used. So if a client sends in 500 pictures and we only use 10 in the brochure, i will not save the other 490 pictures when the work is delivered and paid. It is only my actual deliverables that i am backing up. I will also remove all draft PPTs, DOCs, etc we used to complete the job when all the content has been pulled from these.
- For larger clients with ongoing work spread over many years, i actually guarantee 3 to 5 years of backup for everything delivered, included in my fees. This is something we write down in the contract and i will have two identical copies of every job on two separate hdd drives, and in some cases even a third cloud backup. The clients know they are paying for this. Some clients actually require me to upload every deliverable to their internal ftp with no exception, but that is also something they are paying for.
- For smaller or one-off clients, i will also back up their files indefinitely, but generally tend to clean these up gradually after 3-4-5 years if no other contact has been made for additional work or there is no contract or clause forcing me to keep the files forever.