Level Transmitter Displacer Type

What make & type, of displacer type level transmitter, you are referring to?

Probably one that must be immersed in the fluid it is measuring.

That's a good possibility.

The manual is correct: the displacer must be fully submerged in the process liquid(s) in order to measure the interface between two liquids. If it were not, there would be no way to discriminate between a change in interface level versus a change in total liquid level.

This is really a process control problem, not a transmitter problem. The solution is to fix or regulate the total liquid level so that it will not fall below the upper nozzle height of your interface level transmitter. A second level transmitter and control loop sensing total liquid level (above the interface transmitter) could be used to regulate total level so that it would never fall down into the range of the interface transmitter. Alternatively, an overflow pipe or weir could be used in the process vessel to ensure that the total liquid level must remain above some fixed point above the interface transmitter.

Without knowing anything about the process vessel, the liquids involved, or the application, it is impossible to prescibe a practical solution for you.