So if you have are sure you have a black tank. And if that tank is not holding water but rather letting the liquids drain out. Then yes you need to get that issue (probably the valve) fixed as soon as possible. Right now the liquid is draining out of the tank and the solids are staying behind and piling up on the floor of the tank. If this is not addressed you will soon have the dreaded pile of poop under the toilet and another plug to clean out.
The valve itself might still be functioning and the seals are melted. But with the possibility of melting damage on the valve itself I would probably just spend the extra $10 to replace the entire valve.
Valterra valveCamco valve