Not entirely true. NONE of the people you've mentioned have said that to keep trusting in God, is a works-based gospel...
YOU have maintained all along that we need to "keep presently believing" in God. Problem is, when we have that initial belief on God, we are saved. Once and for all, not just until we screw up and He takes it away.. After we're saved, it's a natural thing to want to keep believing in God.
HOWEVER, just because you "presently" believe today, then what about tomorrow? You don't know today, whether something will happen to rock your faith so much that you stop believing tomorrow.
Only God knows why a person stops believing, and if it's temporary or forever. I've had things happen to me that shook my faith so hard, that I walked away from God for awhile. But I never stopped believing in Him.
A person needs to keep believing in Jesus, that's true. BUT NOT TO STAY SAVED. It's natural to keep believing. But YOU do it for the purpose of keeping yourself saved on a daily basis. And that, is what Dcon, EG and whoever else, calls a works-based gospel. Because it is, because you're working to stay saved. But Jesus already paid that price. So switch your mindset from "okay I gotta believe to stay saved, and I gotta believe tomorrow".. Switch it to "thank God Jesus died to save me from all my sins".
Stop trying to do the work that Jesus has already done for you.
By working to keep yourself saved, you negate what He did on the cross. That's the precise reason that He died, to save you, and me, everyone, from their sins.