I'm so sorry, been there done that and it's so hard.
Don't look at it as giving up, think of your dad accepting his future with grace.
Spend as much time with him as possible, spoil him in whatever way you can. My mom's best friend sent in baked stuffed lobster - one of mom's all-time favorites - and I have a lovely, bittersweet memory of my dad spoon-feeding the lobster to Mom.
So whatever your dad likes best, give him as much as possible. Movies, pet visits, backrubs, beer - whatever! It's ok to be sad, it's ok to cry. But think of the rest of your dad's time here as a "going away present", and store up memories for yourself.