1) have you tried scanning your old HDD for damaged clusters etc
2) Is the power supply sufficient, if its a relatively low power supply say 220W, you may have a bit of a drain that causes the power supply to shut itself off safely rather than burn out... this would then rest once it had sufficiently cooled. Another symptom of this would be it occurred more frequently when you were doing a ot of disk based or virtual memory based tasks... also if you have a new Graphics card, again this could be additional strain... you can normally get by with just a 220W, despite what they say, but in some cases its not always that way... in that field I am no expert but different disks etc draw different wattages and so its a sort of trial and error area... IF it is an extremely low wattage power supply, you might want to buy one thats say another 50W on top of what you already have (no need to go overboard as to be fair a 500W aint gonna get you any better performance if you can make do with a 350W)... failing that, maybe its that your master drive is absolutely chock a block and starting to have difficulties.
Possibly the secondary HDD is in need of a complete reformat, this could definitely be the case if there was for example a clash of file systems...