Fine, then.
Saying 'I'm busy' is an excuse. It does not tell you how much the person can do. It is sufficient reason, unless you're assuming the worst of someone, for any followup indicating why they might be posting less for a period. There is no reason to need more details; people are entitled to privacy. Not including some indication of what this can mean is stupid, because nobody else is a mind reader, but it is sufficient reason. I do not, however, know of many people that will interpret 'things are busy' to mean 'I don't like you and don't want to play with you'.
'I don't have time to' is the same thing, in different words. It makes no difference.
Also, you bring up Osaka, yet you're assuming that I haven't seen incredibly inactive threads. Well... this place moves faster than most things I've seen and taken part in. >_>;