Fully recovered Ebola patients are in general no longer infectious, but there are exceptions.
Isolated cases have long been reported if virus persisting in the eye and in sperm. Now there is a definitive study showing both persistence and active infectiousness in sperm at least 2-1/2 years after recovery, with no reason to think that infectiousness might not continue indefinitely. https://www.sciencesetavenir.fr/sante/ebola-le-sperme-peut-proteger-le-virus-pendant-2-5-ans_125545
From a public health standpoint the sperm of recovered patients is a reservoir from which Ebola disease can re-emerge into the population. This isn’t a huge deal since periodic recurrences were already to be expected from animal reservoirs. It is of concern, however, that outbreaks from sperm infection would likely occur in densely populated areas rather than in the remote jungle villages that are most exposed to wild animals. It also means that countries with no animal reservoirs, and no experience with Ebola, could have outbreaks arising from a visiting or migrating survivor. A sexually active survivor could unknowingly infect multiple partners over an extended period since he himself will not fall ill. Public health agencies need to be vigilant to identify and snuff out any new outbreaks stemming from this source. On the other hand, the lack of such outbreaks so far is somewhat reassuring.
Testing of male survivors might allow concern to be lifted from some and focused on others. Surviving males, unless definitively tested negative, should be strongly encouraged to use condoms. They and their partners should be encouraged to promptly report any suspicious symptoms (though the same pattern of fear and denial is likely to recur in future outbreaks). The right of survivors to medical privacy will be in tension with public health concerns. Survivors known or suspected to be infected could be unfairly ostracized and stigmatized.