It's not always a cut and dried answer - depends on your agreement with the developer, really.
But as someone who has been on that end of things on a custom project: You can't always predict what issues will crop up in a custom project. It's not always something you can anticipate exactly, especially if the scope changes during the project. Troubleshooting/bug hunting are necessary parts of development. If it is beyond what was budgeted for the project, then it's billable time. But that should be communicated, no surprises.