MacBook fails to write to disk after about one hour of use

I'm not clear which computer we're talking about. The A1181 Mid 2009 MacBook is not a Unibody model; it has a removable battery (I'm writing this post on that model right now). The A1342 Late 2009 and Mid 2010 MacBooks are Unibody; they have no FireWire port, and no removable battery. When you open up the About this Mac window, what does it say you have? Instructions and parts for each variant will be different.

The MacBook writes to the hard drive successfully for an hour or so, and then it...what? Writes incorrect data? Fails to write at all? What are the symptoms of the issue?

I'm also curious about the timing. How are you detecting the problem, and how do you know the problem isn't occurring in the hour beforehand? What is your error detection method?

Do you get the same issues when writing to an external USB drive? Or to a network drive?

For the sake of diagnostics, open your Energy Saver system preference and uncheck the checkbox marked "Put the hard disk(s) to sleep when possible", at least in the Power Adaptor section. Sleep is often problematic with hard drives; the hard drive spins slower to save electricity, and then fails to come back up to speed when needed.

Assuming that the problem is intermittent, and entirely drive-related (which seems to be Apple's assumption, or they would have replaced something other than the hard drive), it sounds like a hardware problem. One possibility is a damaged hard drive cable (non-Unibody/Unibody), which may need to be replaced. Open up the computer and take a look at the cable; check to make sure the connectors are firmly attached both to the drive and to the logic board. If the cable looks frayed or twisted, or if either of the connectors look damaged, or if the logic board socket has any bent pins when you remove it, those are red flags.

If Apple replaced the drive recently (within the last 90 days), then the work is still under warranty. You should go back to the store and have them replace the cable. If that's the source of the problem, they should have found it to begin with; if they did a sloppy install, then it's their responsibility to fix their work. The Genius Bar is not infallible; if we don't force them to live up to the standard they claim for themselves, then everybody suffers.