How long does a bonus last?
Till the end of the current invasion. Cyborg reads:


  During an invasion involving the Cyborg, you may spend 1 Energy to add +1 Ground Strength to every Infantry Unit in that invasion.


The rule book defines an Invasion as:


  Invasion: In order to add new worlds to his Empire, a player must launch Invasions. A player performs an Invasion by discarding enough cards from his Warzone to match the Fleet Strength and Ground Strength of the World he is invading.


So, the saved Ground Unit will only get the +1 bonus during the current invasion (cyborg's rules text). The Med-bot can save the troop from being discarded, but the bonus ends immediately after the current Invasion that Cyborg is participating in.