how one can keep the time of sentinel 1 GRD file after processing NDVI using SNAP?
You found a bug in the NDVI processor. It is not copying the time information. It will be fixed with the next release.
Beside this, it is not very meaningful to use NDVI on Sentinel-1, I think. It is intended for optical sensors.
You need two bands, one of red wavelength and the other in the NIR spectrum.