Below is my list of tips and suggestions. I've arranged them in the order I'd personally approach this. Hope it helps.
What you're describing could be a cabling problem. You said the drive eventually conks out and reboots don't seem to help, but complete resets do. I can imagine this behavior could occur if you have a seldom-used pin on your IDE cable that's faulty. Or a pin that only temporarily fails under certain thermal conditions. I can also imagine this being many other things, but IDE cables are often easy/cheap to replace. You may even be able to use the one from your CD drive, just for testing. It may well not be this, but if it ends up being this, you'd obviously kick yourself for not trying this early on.
You should find a program that can give you the SMART status report on your drive. I live mostly on Linux and I like to use one called "gsmartmon" for this. You can perform SMART tests to get more evidence of the health state of the drive. Some BIOSes may even have a UI for this, not that I've ever actually seen such a BIOS. (Edit: Many drive manufacturers also have their own custom diagnostic tools you can download, you should look in to that too).
Switching IDE ports:
You could also try switching the location on the motherboard your IDE cable connects to (provided you have a separate master & slave connector for IDE drives). It's unlikely, but if there's hardware damage to your motherboard, then you may have a case where as the system heats up, a fault occurs and the drive can't be used. Switching IDE ports on the board doesn't prove or disprove this necessarily, but trying it gives you a tiny bit more info.
Capacitors can fail in visible ways. It never hurts to check for failed caps.
It's possible that your power supply is the culprit. If you have a power supply tester, you may want to give that a whirl. You may also want to try to increase the IDE start up delay in BIOS, though that doesn't REALLY sound like what your problem is.
As you state, obviously another thing to try is another drive. But as you also said, that costs. So I suggest you try the above first, obviously.