What is the maximum allowable time for an athlete with a suspected heat-related illness to rest before resuming activities?

When dealing with a suspected heat-related illness, the primary concern is the athlete's health and safety. Resuming activities should only be considered when the athlete is fully hydrated and acclimatized. This is crucial because heat-related illnesses can lead to serious complications, including heat exhaustion and heat stroke, which can be life-threatening if not managed properly.

The recovery process involves more than just a set time frame; it requires the athlete to rehydrate adequately and allow their body to adjust back to a normal physiological state. Factors such as the severity of the illness, the environmental conditions, and the athlete’s individual response to the heat all play a significant role in determining when it's safe to return to activity.

In this context, other options suggesting specific time periods can be too rigid and may not account for the athlete’s specific condition or response to treatment. Hence, focusing on full hydration and proper acclimatization is the most appropriate approach to ensure the athlete’s safety before resuming sports activities.