I clicked to do the bug catching and so far haven't seen the requested insect but then my browser has been crashing A LOT. So I'm wondering if the beetle I needed appeared on a page only to have the browser crash repeatedly, do I lose the bug or does it re appear later on?

If you miss the bug on one page it should reappear again (eventually) on another. You shouldn't need to quit the bug quest or buy one. I hope you get your browser issues sorted out! c:

Thanks. I'm trying to work towards a new computer but atm bills wiped out my original lot of savings.

I don't think you can quit the bug quest. You either find it or buy one and pretend you found it. But until you show her the bug she asks for she won't give you a different quest.

It is my experience that the bug will reappear. However, this year's bug catching will end tonight.

NPC Councilor Chamalma is like the Atebus Revolution Historical Society, she doesn't forget. Just like your unanswered dance invitations save over from year to year, she will continue to ask you for the bug she last asked you for when it is once again bug catching season.