I have ME. You are darn well not being unreasonable. It's a chronic illness. Your immunity is compromised. Just FYI. This is what I do:
Taking echinacea 2 weeks on, 2 weeks off (otherwise the body gets used to it and ignores apparently)
Taking vit d, massive doses right now as we are at the worst time of year because our natural supplies of vit d run out around Xmas assuming we've assimilated enough in the summer (nutri one with k2 is very good)
Drinking small amount apple cider vinegar (with the mother) this often kills colds. At the sign of the cold, drink a small amount in water 3/4 times a day. Get it from Amazon, I use braggs.
If the cold is a really bad one, I don't manage to kill it with acv, I'm guaranteed to get a cough - have one now. It goes to sinusitis quickly. This happens once or twice a year. I now have a nebuliser and saline solution (can buy nebuliser online/Argos, contact lense saline solution in supermarkets or make your own). Use the nebuliser 3 x/day circa 15 mins.
There is a lot of online information proving the effectiveness of saline solution for killing coughs, bronchitis, loosening excretions etc. Your dad should maybe try one. And I believe they should be given by the NHS tbh to people, who suffer ailments such as chronic bronchitis.
Next time I have a cold, I'm going to start using it earlier to see if I avoid the cough altogether as salt water gargling is also recommended for colds. Nebulising gets it into the nasal and chest cavities so even better.