Hide a service without losing its history

Open Menu, then SETTINGS, then Service menu, tap Edit on the service, and turn on Hidden.

The app states the trade directly: hiding a service takes it off your booking page, and past appointments and invoices keep it.

That is why hiding beats deleting. Your reports for last year still make sense, old invoices still say what the client actually paid for, and the service simply stops being bookable going forward. Use it for anything seasonal, anything you are phasing out, or anything you only offer to certain clients.