It is very interesting to read the contributions to this thread. I do not think of it in terms of "how many hours" of conditioning.
Conditioning is the 5th event and is a means to be successful at the other 4. At it's most efficient it would be individualized for each athlete.
My application: General conditioning is scheduled for each group. The schedule varies from 30-45 minutes. This is for general conditioning.
Pre-team-L5: Philosophically, I follow the policy that pre-team thru L5's condition, condition, condition, condition when they are not working on routine skills or needed upgrade skills. How much time, really depends on the time of year and athlete. These groups do specific skill conditioning on events. Their tasks do not change much, but have small variances to keep it interesting/tolerable.
USA-G Optionals: For the L6-9's they have the same General Conditioning schedule, but their Event TBC (To Be Completed) sheets have a higher load of specific skill conditioning. The load of TBC's changes throughout the 52 week cycle every 6 weeks. The specific tasks can change as per coach and the conditioning focus changes throughout the week. Athletes can check the pre-printed sheets and work them while completing their event workout. Cycles are high, moderate or low intensity conditioning. If I added up the time, I suppose it would be a very high percentage of the workouts some times of the year.
In the gym, we recognize and reward strength/skill gains. The gymnasts are aware it is a necessary part of what they love to do. If the athlete is aware of "why" (making it personal) and that they are making progress the cycle of fitness is ever changing.
I hope I have contributed to the thread. Best from this short balding coach, SBG -