The phrase "after they maintained" is correct and usable in written English.
It can be used to indicate a sequence of events where something was done following the act of maintaining something.
Example: "After they maintained the equipment, it functioned more efficiently."
Alternatives: "following their maintenance" or "subsequent to their upkeep".
The Englishmen won three holes out of four from the ninth to go two up after 12, an advantage they maintained until the 16th when Rose missed a five-foot putt to allow the Americans to win with a bogey.
How are they maintained after the treatment has been stopped (which is really the relevant question) is unknown.
The mutant parasite clones did not show an obvious growth phenotype, although it was noted that they grew extremely synchronous even after three growth cycles they maintained their synchronicity.
Police do not know who had brought the gun, but they maintained that after the struggle with Mr. Soto, Mr. Alvarez seized it and fired at the officers who had arrived.
He joined the Old Catholics (Altkatholiken), those who separated from the Vatican after the council but believed they maintained Catholic doctrine and traditions.
But lawmakers from both parties said Bush is trying to dictate war policy after he leaves office, and they maintained that an agreement with such enormous consequences should be submitted to the Senate for ratification as a treaty.
Benzema went close twice more as France gained some momentum before half-time, and they maintained it after the break as Yohan Cabaye, Paul Pogba and Blaise Matuidi gained control of the central areas, allowing Griezmann and Valbuena to cause damage from wide.
The eggs begin to heat up to the temperatures required for gestation to begin only after they have maintained contact with the mother's brood patch for hours at a time.
For the professional record, the questionnaire was comprehensive, including such questions as when the student decided to pursue engineering, how they obtained their first position after graduation, did they maintain an interest in "liberal" study, whether or not they have found it necessary to study after graduation, how satisfied they are with their current position and/or prospects.
