Though it wasn't ever mentioned on the show, I kind of got the feeling that his new wife/girlfriend at some point around Season 2 or 3 gave him some sort of, "It's me or them," ultimatum, possibly coupled with starting a new family. Under those circumstances, it would be understandable, if totally inexcusable. Also, it was mentioned that he and Wife #2 had moved to Europe, for reasons unknown. In a situation like that, coupled with, almost certainly, starting a new job, if not a whole new career, it actually might have very difficult, or even impossible, financially, to get back to the U S. Apparently, he couldn't or wouldn't either return when Joyce died or continue with financial support for Buffy and Dawn. Then again, the terms of the divorce might have included a one time settlement rather than monthly child support.
Has it ever even occurred to anyone that Hank might not even know that Joyce was dead? It was mentioned a couple of times that there wasn't any communication between Hank and his children, inexcusable in itself, but that might be a possible answer to his "parenta absentia" (if that's the proper term and spelling) role at such a time. If he didn't know, and if the settlement had been a one term agreement, then his main offense would be somewhat more understandable, if once again, inexcusable.
I am in no way trying to defend Hank Summers' actions here. As a parent, he would have an obligation, morally, if not legally, to be reasonably sure that Buffy and Dawn were properly cared for under any circumstances. As I have said twice before here, doing anything less is inexcusable. But there are circumstances and conditions that we are totally ignorant of that would have to be considered before we decide exactly what Hank Summers' actual offenses were. He was definitely wrong, but we really can't judge, given what evidence we have, just exactly HOW wrong he really was.
(Just as an aside here, I can't help but wonder, given Sarah's attitude toward her own father, who she refers to as simply "the sperm donor," if she might have had some say in how Buffy and Hank's relationship developed)