See also What are the advantages and disadvantages of thinner PCB thickness (<1.6 mm or 0.063'')?What are the advantages and disadvantages of thinner PCB thickness (<1.6 mm or 0.063'')?
My PCB manufacturer rep was showing off some 0.5mm PCBs recently. The panel was distinctly floppy, but the individual boards were coin-sized and apparently worked fine.
This is the main limitation, and is hard to answer either way without considering the mechanical design surrounding the PCB. Is force applied to the PCB? (connectors, switches) How large is it? Does it have mechanical support once in its casework? Are there any long thin components on it that will cause problems if it flexes?