That is usually a sign of a broken harddisk, given the specific circumstances it might however be a side effect of insufficient power supply to the disk or a broken cable.
Yes the routers esata port will not deliver the "normal" esata max spec power, so only low powered 2.5" disk's will work. So you either need a case with separate power or alternatively use a SSD.
PS: On the wrt1200ac esata will work better for transfer speeds (70 MB/s vs 115 MB/s), compared to usb3.0, so its worth the hassle.
I'm currently using a 2TB LaCie Two Big eSATA & USB 2.0 external HD; the eSATA cable is new and I've been able to connect it to the Linksys using the USB port.
Do you think that I'm missing any packages or there is a configuration settings that need to be adjusted?