When a Sith essence transfers, do they lose their ability to use the Force? I would assume so, because their midi-chlorians would be left behind, wouldn't they? If a Sith Lord used clones, as many Sith did, they wouldn't be able to use the Force, would they?
Midi-chlorians exist in the cells of all living things, including clones:
Midi-chlorians are a microscopic lifeform that reside within all living cells and communicates with the Force...Without the midi-chlorians, life could not exist, and we would have no knowledge of the Force. They continually speak to you, telling you the will of the Force.
Qui-Gon Jinn, Star Wars: Episode I The Phantom Menace
One's strength in the Force is determined by the concentration of midi-chlorians in one's body, and evidently a clone body contains the same concentration of midi-chlorians as the original since there are numerous examples of Force-sensitive clones (such as Palpatine's clones, Set Harth's clones, and Galen Marek's clone). Consequently, a Sith who transfers his essence from his original body to a clone of his own body would have the same Force strength as before, despite the fact that his original body and its midi-chlorians would be destroyed by the process. His connection to the Force would be through different midi-chlorians.
Every instance of a Sith attempting an essence transfer has either been into one of his own clone bodies (e.g. Palpatine) or into another Force-sensitive individual (Darth Bane, for example, who attempted to transfer his essence into his apprentice, Darth Zannah). Either way, the new body would have a high enough concentration of midi-chlorians to support a connection to the Force. A Sith who transferred his essence into a person who was not Force sensitive would likely lose his connection to the Force. The lost connection would be permanent, because a Force-insensitive body cannot be made Force-sensitive.
When the Emperor transfers his essence into (various) clone bodies in Star Wars: Dark Empire, it's apparent that his ability to use the force is undiminished.