Is there a specific period for returning a greeting, such that the obligation to respond is forfeited if the person delays beyond it, or must the greeting be returned even if a long time has passed?

Returning the greeting (Salam) is obligatory and must be done immediately. It is an individual obligation (fardh 'ayn) if there is only one person being greeted, or a collective obligation (fardh kifayah) if there is a group, in which case the obligation is fulfilled if one of them returns the greeting. It is a condition that the reply be directly connected to the greeting, without a long pause or extraneous speech. If the reply is delayed, it is no longer considered a response to the Salam, and the person would be sinful. This also applies to a Salam sent via a messenger or a letter.