Is there a chance of any sexually transmitted disease to recur even after been treated?

Only if the treatment was not completely effective. The dangerous one in that context is syphilis. The intital outbreak only produces a little hard place that will go away in a short while. It will then produce a rash that doesn't itch and often goes unnoticed as an STD but will sometimes imitate other diseases. After those symptoms disappear, if untreated, it will appear to go dormant but continues to work on critical organs. In it's final stages it can cause very serious damage and even death.

At any of the above stages it will show up in testing. If you have been treated for syphillis, it is a good idea to be retested later to make sure the treatment was complete.

Genital herpes produces repeated outbreaks that continue over time. There is no cure for herpes, only medical treatments that help you live with the symptoms. HIV (AIDS) is yet uncurable also, however there are some gene therapy treatments that show promise.

Also, I'd add HPV and some strains of hepatitis to that no cure list in paragraph 3.

If you believe you're experiencing some sort of recurrence now, you should abstain and see a doctor.