We are in the process of buying and we've just been away (long haul).
We made sure that the agents/solicitors/surveyor were informed of this and what the time difference was so that we didn't get any unexpected calls in the middle of the night, and to make them aware that we might not always respond to emails straight away.
We managed to deal with the survey report which came by email, we have raised several queries via the solicitor and finalised the fixtures and fittings negotiations. We also had scheduled calls with the surveyor and with the agent despite a significant time difference.
No viewings were requested for our property while we were away, but if they had been then we could have OK'd them and arranged for someone to come and give the house/garden a quick once over before the visit. We have just gone with a second agent and we also managed to liaise with them to take the photos and get the listing on-line. We did the signatures for the revised multiple agent fees on-line.
It's pretty poor to be "unreachable" for extended periods - especially in this day and age. Yes, we would have liked to just enjoy an uninterrupted holiday, but we would also like our sale to progress and would have wanted to know about any viewings/offers on our current property.
There's not really much you can do other than to leave the offer on the table, but it would raise concerns about how serious they were about progressing what is already a long and convoluted process in a timely fashion!