It cannot be recharged by itself. The voltage can still increase after you have removed a consumer, but in no case after it is almost completely empty. I think you have a connection problem. First of all, check the connection to the earth next to the battery and the condition of the connections to the fuses on the battery (they look like blades attached with screws). Unfold them, clean the oxides well with contact spray, then put them back. A multimeter would be helpful in locating the problem.Do not replace the alternator unless necessary.