Hi,
Storing the time part of a Date is not supported in the DBF3 specification (Shapefile uses that).
However, you can setup a system property to enable that. You may find more details on the shapefile plugin page.
Quoting from that page: Dates do not support the storage of time by default. If you must store time stamps and do not need interoperability then you can enable the storage of time in date columns by setting the system property org.geotools.shapefile.datetime to “true”. Almost no other program will be able to read these files.