[Felix The Assassin]

Your symptom falls into a two problem approach.
First and foremost:
1. Check and clean both drives at BOTH the power supply, and IDE cable plug-ins. And while your there check to make sure one is master, and one is slave on the DIP panel.
*FYI: Bad IDE will cause the system to freeze or slowdown on boot up as the POST is searching for components plugged in. Bad or interrupted power will cause the component to drop of the peripherals list under the OS.

2. Check and gently clean the MB where the IDE cable plugs into it.

Second:
1. Swap the IDE cable.

Couple more things to do: I'm assuming widoze OS?
1. When it fails again, go into system resources, and look to see if your drives are dropped there. If not, how many and what color are the attention icons?

2. You might have to do a PS test. Try different configuartions of plugging the leads into different components until you either:
A) Find the faulty lead.
B) Find that the PS is not the problem at all.
Then refer back to swapping the IDE cable.

Lastly, it could be dust, or loose connection causing this entire situation. (Been there, done that!)