I would document the incident, including timelines. The time that the database was offline has an associated cost. That is what you need to use when someone says that they can not afford hardware resources for backups.
Backups are insurance - you have a risk (losing data). To reduce that risk, you pay a premium (the costs of setting up the backups). And you hope that you never make a claim (database failure) but you sleep better at night knowing that you have managed the risk.