持続 and 維持: continuing an activity and maintaining a condition
Compare exercise or effects that continue with health or a bridge that is maintained. Preserve the exercise plan, the open question about duration, and the inspections required for maintenance.
An activity or effect continuing over time
持続 (じぞく) includes continuation and persistence. 「運動を無理なく持続するため予定を立てた。」 means “I made a schedule to keep exercising without overdoing it.” The schedule was made for continued exercise; the sentence does not report that a long period of exercise has already been completed.
「薬の効果がどれほど持続するか研究している。」 means “We are studying how long the medicine's effect lasts.” The thing continuing is the effect. The duration remains a question under study, rather than a specified period or a settled research result.
Maintaining health or a facility
維持 (いじ) includes maintenance and preservation. 「健康を維持するため毎日歩いている。」 means “I walk every day to maintain my health.” Read the ongoing walking and its health-maintenance purpose without adding a guaranteed improvement in health.
「古い橋の維持には定期的な点検が必要だ。」 means “Maintaining the old bridge requires regular inspections.” The maintenance target is a bridge, and the sentence states a required condition. A need for inspections does not report completed inspections or repairs.
What continues and what is being preserved
For 持続, identify what continues over time; for 維持, identify the condition or function being preserved. Continued exercise and maintaining health can be connected, so the two perspectives can occur together. Do not allocate every activity and every facility exclusively to one word.
A purpose of preservation is not an already achieved change to stability, and continuation need not concern a fixed numerical value. Keep a plan's purpose, a current activity, an open research question, and a required condition separate. Read only the duration and result that the sentence actually states.
How do the open question about how long an effect lasts and the inspections required to maintain an old bridge differ?
Show the answer and why
The first retains an open question about the duration of an effect. The second states a condition required for maintaining a facility. Neither establishes a settled duration or completed inspections.