Is dad by any chance in a home? Are you by any chance feeling guilty for being so far from him?
Not wishing or trying to be "horrible", but I wouldn't be surprised if you answered "yes" to both questions. We're all only mere humans, aren't we?
What's the point in sending dad a card if he has dementia, as you have hinted at? He obviously won't be able to appreciate it, will he? So if you want to do it simply to try to ease any guilty conscience, if that indeed is your motive, I shouldn't bother.
These terrible things happen to loved ones but your love for dad is far more important than any card. Your own conscience is something which only you can deal with, though. But sending him cards cannot, sadly, improve his health. Just keep loving him for as long as you have him.