Have you checked the fuses?  There is an always hot wire that runs
through the accessories (like the radio and clock) to keep them
running, as well as a switched hot wire that enables thing that are
only supposed to run when the ignition is on.  It sounds like you have
blown the accessory fuse.

If you have recently put in a new radio or otherwise modified the
accessories, that would be the first place to look for a wiring
mistake.

Measure the battery voltage when cranking the engine.  The voltage could
be going down too much thus resetting the clock.

Defective ground and battery cable connections could cause the same problem.

Good luck and let us know what fixed it!