I guess one third to one half of the ideas that get pitched stay together for at least 4-6 weeks, refining the product/pitch or applying for local funding (e.g. accelerators, pitch contests, etc.)

The main objectives seem to be recruiting and networking. Startups that stick are a bonus.

That said, I think the app/software ideas get a little more done in the weekend, in the sense that meaningful hardware hacking is hard to do if it wasn't planned. Judges seem to be impressed by hardware, perhaps for that reason.

I have participated in a few healthcare-related hackathons in the Boston area. A few things I like:
-forming my own teams
-access to a wide array of experts (MDs, engineers, MBAs, PhDs, etc.) who represent different parts of the problem (clinicians, marketing people, insurance industry, etc.)
-lots of snacks and caffeine (seriously)
-easy internet access
-lots of power strips
-conference rooms with TVs or projectors
-close access to supplies for hardware hacking (materials, tools, hardware, etc.) -- my team needs for this were met by my lab at MIT
-clear guidance on rules (software only? business model required? 100% new ideas only?)

The general structure that seems to work for the events I have attended:
Day 1
-Intro, ground rules (re:IP, prizes, judging, etc.)
-First round of pitching (pitch the problem or idea)
-Mingling
-Second round of pitching (solution, team nucleus, brand new ideas, etc.)
-Mingling
-Work, mentors circulating (entrepreneurs, VCs, hackathon veterans, etc.)
--
-Work, mentors circulating (entrepreneurs, VCs, hackathon veterans, etc.)
-Pitch presentations
-Judging
-Prizes

I hope that helps.