Hello,
welcome to the 'Ask a Doctor' service.
Unfortunately the information you've provided is not enough to determine any diagnosis. I have some thoughts though and I'm going to share them with you.
Let me start from the infection itself. Having taken antibiotics usually means that the infection has been dealt with. If he still has
fever or other signs of active infection then a new medical assessment is required. The
cough and other symptoms like post-infectious
fatigue may persist for a while even when the infection is gone.
The
steroids may also cause some fatigue for various reasons. Muscle wasting, electrolyte disorders, direct effect on a patient's psychology, etc to name a few.
Sometimes old individuals need time to recover from any acute condition including infectious diseases. Perhaps this is the case with your father. Clinical assessment and appropriate laboratory testing may identify other potential causes.
I hope I've answered your question. Please let me know if you need further assistance.
Kind Regards!