If your kids aren't interested in contacting their father, and their father isn't interested in contacting them, there's really no problem. They have a loving stepfather. You've done all you can to maintain the relationship between the kids and their dad, it's time to let it go.
If the problem is the dad calling every once in a blue moon and upsetting your kids, then next time just tell him: "I'm sorry, but it just upsets the kids when they hear from you like this," and ask him (gently) to stop calling if he's not going to be in their lives consistently. This is not being mean, this is just protecting your kids and putting their interests first.
If the problem is that the kids want a relationship, and their dad doesn't, tell them "it's nothing you did wrong, your bio-dad just wasn't ready to be a father. But luckily, you have a (step) dad who loves you and isn't going anywhere." If you stop trying to singlehandedly keep the bond alive, I think you and your kids will feel much better. And you aren't closing any permanent doors this way, either. If your kids or their dad feel (or act!) differently in future years, you can revisit it then.