I want to articulate that lot of time is getting wasted while waiting for a reply from this person. So, is there any one word I can use for "time spent for awaiting reply"
The best answer(s) I could offer given the new comment information, since there is not one word to encapsulate the entire meaning asked about, would be some of the following suggestions.
Include in your conversations at the end of the message, something like:
1. Please reply with haste, we are spending too much time waiting on replies.
2. I need a quick response please, these long pauses are causing a huge waste of downtime.
3. Please, there is no time to dally, we are wasting time.
4. Time is precious, please don't dally in your reply.
5. We are continually seeing sluggish responses, let's please remember to hastily reply.
I hope these suggestions will help you. There are many ways to say what you want but basically it boils down to finding some pleasant, however forceful, ways to get your message across that time is of the essence (you could even include that phrase at the end of the message, for example; or at the beginning to emphasize it even more - maybe preface the whole thing that way).
I would also suggest that you lookup something like time wasting synonyms (SOURCE: www.thesaurus.com) to come up with some possibly new ideas for words. But the general idea of what you will want to do to get the point across is what I described above using some flavor of that type.
If you wish to describe the act of waiting for a reply, I would simply use "awaiting [your reply]". I would assume that it is already clear from further context that you are awaiting (the reply from) the person who you are speaking to.
As far as I'm aware, there is no single word to encapsulate the idea of "awaiting a reply for longer than is deemed necessary". Especially if you expect "reply" to be implicitly clear.