Hi Maria38Divine...
I wish I had some great advice to offer... I *do* think depression can (absolutely!) make you not want to hang out with your family. Isn't isolation often a big problem with depression? That, and low energy (not wanting to put in the effort to be around people, even those you normally like)?
That said, it's really kind of you and your siblings to keep up the contact with your dad. (My dad has kind of dropped out of my life as well, and I've tried to stay in contact - but really have found that as I get older, it's too hard for me to have a 1-sided relationship.)
Does it help at all when you plan things out with him farther in advance? Maybe he's not comfortable with having his routine changed, but does better with more time to prepare?
I also kind of wonder... if he's saying that he doesn't want to be a burden, if you could articulate more loudly that you really WANT to spend time with him (i.e. it causes you more sadness to NOT see him)? I'd only say that if it feels true for you... but if he's depressed, he may need to hear that a little more loudly to really get it, maybe?
I guess it's good that he's got people he hangs out with... but I'd find the drinking a little worrisome

. Sorry you're having to figure this out... Good luck!