During a panel at this years LymeMIND conference a representative from the CDC named Susanna Visser said that she and her team absolutely believe in persistent Lyme, and that the CDC website now acknowledges it on a basic level.

>Why some patients experience PTLDS is not known. Some experts believe that Borrelia burgdorferi can trigger an “auto-immune” response causing symptoms that last well after the infection itself is gone. Auto–immune responses are known to occur following other infections, including campylobacter (Guillain-Barré syndrome), chlamydia (Reiter’s syndrome), and strep throat (rheumatic heart disease). Other experts hypothesize that PTLDS results from a persistent but difficult to detect infection. Finally, some believe that the symptoms of PTLDS are due to other causes unrelated to the patient’s Borrelia burgdorferi infection.

"Other experts hypothesize that PTLDS results from a persistent but difficult to detect infection." https://www.cdc.gov/lyme/postlds/index.html