Do my certificates have to stay current for the Sports Trainer insurance to apply?

Yes. An SMA article on Sports Trainer insurance warns that "you may not be covered by your Sports Trainer Insurance policy" if any certificate required for your accreditation has expired while you work as a Sports Trainer.

The article lists these renewal frequencies:

• Level 1: CPR yearly; first aid every 3 years.
• Level 2: CPR yearly; first aid every 3 years; the emergency care for suspected spinal injury certificate (PUAEME004A) yearly.

The article was published in 2018 and says its information was correct at that time, so the policy limits it lists (for example $20 million public liability) may have changed. Treat the currency rule as the main point.

Source: https://sma.org.au/important-information-sports-trainer-insurance/