Typically, when the Test/Reset buttons don't operate as they should during a new install, it tends to be the result of Line/Load reversal. Be sure that your hot wire +neutral is wired to the brass and silver terminals, respectively, on the LINE side. Anything downstream should be wired to the LOAD terminals. The terminals don't always match up between old and new GFCIs so it doesn't hurt to check. If you can confirm the device is wired properly, and it's still behaving this way, it's possible there's either a ground fault somewhere downstream (shared neutral possibly), or that the device may not be performing to specification, and thus need to be replaced.