First off, I would suggest copying the data off the drive and onto some other medium as soon as possible. It's possible that you are seeing signs of physical or electrical failure, and if you are, there is very little that you can do to "restore" the drive to normal functioning; in that case, the drive will likely continue to semi-function for some time, and then at some point simply fail completely.
My first concern would be where exactly the voltage drop occured. Was it at the power supply input terminals (AC line voltage drop/brownout/blackout), or was it at the drive (faulty power supply)? ATX PSUs are regulated to within rather tight specifications, and the hard drive might just not deal well with a gradual voltage decline at its power input terminals. A regulated power supply will provide a steady voltage until the input voltage gets down to its cutoff point, at which point it will generally cut power completely (similar to when you turn the computer off via the power switch forced shutdown). Since an external power supply connects directly to the drive, I would expect it to be regulated to within the same standards, but if it's a cheap one, or for that matter simply old, it might not hold up to the varying power demands of a hard drive.
A gradually decreasing voltage fed to equipment that expects a well-regulated voltage can cause any of several classes of problems. The two I see as most likely (if this is indeed the problem, which is far from certain) are that either the spindle motor took a hit, or that as the voltage fell some component started to self-oscillate which in turn caused (physical or electrical) damage.
The drive may have trouble spinning up and keeping the correct speed (spinning platter hard disk drives need to maintain a very exact rotation speed), and might be detecting its inability to properly read data off the medium, power down, re-start and retry the read, possibly multiple times. This would explain the long delays in reading data.
Media damage due to non-parked heads is another possibility, but seems significantly less likely. If there is physical media damage, you need to get the data off the drive right now as it will only get worse from this point on.