1999 Honda Civic radio fuse problem

Does the radio have to be turned on for this to happen?  If yes, disconnect the speakers and see if it persists.  If no, unplug the radio and see if it persists.  If disconnecting the speakers remedies the problem, you could have (a) blown speaker(s).  If disconnecting them does not, you could have a shorted speaker wire.  If you have to unplug the radio to stop blowing fuses, it's probably toast.

If disconnecting the radio has no effect on the blowing fuses, it could be a problem in the wiring leading up to the radio, or a problem with another component that shares the same accessory fuse (or the wiring leading up to other said component).