How does local memory behave when used in autorun kernels for FPGA-based OpenCL design ?

Your observation with the emulator is very strange. It could be a bug in the emulator. Autorun kernels are completely separate modules with no connection between them other than on-chip channels; there is no way the same buffer could be shared between them. Regarding whether data stored in buffers local to a specific autorun copy are kept or not after the copy is restarted, there is nothing mentioned in the documents and I would assume the behavior will be undefined in this case. If you need such consistency, it is probably best if you wrap your autorun kernel in a while(1) loop to prevent it from reseting; of course this could come at the cost of significant area overhead.