There are some things that are simply not done – and are always expected of others – in a professional working environment. Besides the usual (a lack of professionalism, physical and/or sexual harassment, etc.), one of the primary responsibilities for anyone is to reply to emails.
Because PR and marketing are deadline oriented industries, once a specific date has passed, it has passed.
There are always excuses as to why certain requests weren’t replied to. The usual one is “I forgot” (which is a lazy excuse), but they can also be set aside when an inbox is too full (delete spam!) or if the subject heading is misleading (which is another story altogether).
If something needs to be replied to asap, reply asap. If you’re not in the office (or anywhere near email), forward the request to someone who can reply to it.
If it will take more than a few minutes to reply, flag the email if it might get lost in an inbox (or start writing a reply and keep a draft with an “urgent” notation on it that can later be removed when being sent).
In the end, reply to your emails, especially when they’re deadline-related. There are no time machines that will allow for a re-do.