You said you bought it from eBay. Did you buy it from an authorized dealer, or from a private owner?...because that might be a problem, if the seller was shady about not listing any problems with the P910i you just bought. Perhaps it was damaged and the seller just changed it with a new housing and say that it was new...I don't know. But you just have to remember that this is a device. There could be a bunch reasons why your handset is acting up. It could be the mic, the antenna, the main board PCB, etc. Or perhaps it has an outdated firmware.
If you want to just save yourself the hassle, bring it in to a service center that can diagnose your phone. Or just contact the SE service center. The number will be listed on the SE website. However, if you want to do this on your own, try updating the firmware first. If that doesn't work, then try to flash the phone's firmware. If that still fails, then the problem is related to the hardware. But like I said, that's a lot of hassle if you're going to do it on your own. Just contact SE Support and see what goes on from there.