Is it sufficient to bring to mind the intention of making up many prayers and seeking reward only at the beginning of the act of worship, or must it be brought to mind before each prayer that is being made up?

One should have the intention of seeking reward (Ihtisab) when commencing any act of worship. For making up missed prayers, it suffices to have the intention of seeking reward for some of them, and it is not obligatory to specify an intention for each prayer, although that is better. Some scholars are of the opinion that if a person intends to seek reward at the beginning of his day, that intention suffices him for all actions throughout the day, even if he does not specifically renew the intention when performing them.