"Replay" means to play (a video or audio recording) again. You reply to a message. I agree with Rooftops in that "fail to" is a little harsh. It makes you sound like a terrible person who deserves to be punished. Your tour guide is correct in using "don't" to mean a simple fact. But hey, whatever floats your boat. :) My rewrite: "Dear customer: if I don't reply to your message promptly, I am probably out of the office for a moment. Thank you for your patience." The use of "must be" cannot work here, as it sounds like the person doesn't know what he/she is actually doing.

'If I fail to" sounds a little austere or severe in a sense where it may not be required in this context. In terms of authenticity both seem to be right! A small correction: "If I don't *reply* *to* your messages *on* time, I must be out for dinner, please wait a couple of minutes." But of course this does not change the understanding of the message! Good luck!