I've not given up on a build, but I have lost interest, which is pretty much the same thing.  The build goes to the Shelf of Doom, only in rare cases to be picked back up again and finished.

It can be that I just don't feel like working on it, or I run into a technical hurdle and stop to think about it, or the kit isn't what I thought it was when I opened the box.  Search the Ships forum and you'll find my USS Pennsylvania build.  That's got a little bit of each of those reasons, and it's been sitting unfinished since 2010.  I will probably jump-start it some day, because I don't like to start something and leave it unfinished.  But I may die before that ever happens, too.  You never know.

On the other hand, in my one club, we have an annual build theme, due by our December meeting. A couple of years ago, we decided to make the theme, "Shelf of Doom".  You picked a SoD build and worked on it, to get it completed by the December meeting.  That was such good motivation, that I wound up finishing 3 builds that had languished for a couple of years.