What indicates that strong acid cation exchangers may need regeneration?

A drop in free mineral acidity is indeed the correct indication that strong acid cation exchangers may need regeneration. This occurs because as the cation exchanger operates, it captures various cations from the water, replacing them with hydrogen ions. Over time, the exchanger becomes exhausted as it has taken on a significant amount of cations, leading to a decrease in the discharge of hydrogen ions and ultimately a reduction in the free mineral acidity of the water. When this drop is noticed, it signals that the exchanger's capacity is diminishing and that it may require regeneration in order to restore its effectiveness.

The other options do not directly correlate with the need for regeneration of cation exchangers. A rise in heat transfer efficiency could suggest that the exchanger is functioning well, while a decrease in water temperature may not provide relevant information regarding the condition of the cation exchanger. A rise in dissolved oxygen also does not relate to the performance of cation exchangers, as it primarily concerns the water's oxidation state and does not address the exchange capacity of the resin. Thus, the drop in free mineral acidity serves as a clear and relevant indicator for the necessity of regeneration.