DMA channel chaining should not depend on debugger.
Is customer uses same project configuration between debug mode and non-debug mode?
Code in debug mode is usually slower, if software contains some issues (such as close a peripheral too early by checking FIFO empty flag instead of peripheral idle flag) that only appear when code is faster, this can happen.
Another possible cause can be the debug host did some additional initialization that is required by the software, but the software itself does not do them.
To track, suggest to add some debug notification in each stage of channel chain; if project is emergent, as a back up, can manually start another DMA channel in DMA IRQ handler