for me...
i'll think more broadly...
has your father has this problems last time?

if not, a suddenly chronic disease like this trigger me something else...
most of these problems are usually self limiting and recover by it own with time...wont last 2-3 months.

seriously, brought your father to general medicine clinic in Hospital and have a thorough body checkup.
just to rule out any causes which may cause immunocompromised...
which immuno compromised patients actually presents as ...prolong flu, diarhoea, chronic cough etc.

how old is your father anyway?