The solubility of potassium bitartrate in water at 20°C is given by Wikipedia as 0.57 g per 100 ml, which is considerably lower than that of sodium bitartrate. Generally, a potassium salt is more soluble than the corresponding salt of most other metals—in particular, more soluble than the sodium salt. For example, potassium hydrogen oxalate is more soluble than the corresponding sodium salt (in H₂O at 20°C). Tartaric acid itself is highly soluble.* Is there something special about tartaric acid, or are there other potassium salts of highly soluble organic acids that have markedly low solubility?
*133 g per 100 ml for either optically active acid. (Curiously, and probably irrelevantly, the racemic mixture has much lower—albeit still high—solubility: 21 g per 100 ml.)