Apple has discovered that a "very small number" of Apple TVs might have issues with WiFi. Because of this, Apple has opened up a replacement program, authorizing Apple Authorized Service Providers or Apple themselves to replace faulty third-generation Apple TV devices for up to two years from the purchase date.
The issues include the device not being able to locate a network, join a network, or being unable to maintain a steady connection to a network. To be eligible for a replacement, your serial number must fall within the range provided by Apple. This means the last four characters must be DRHN and the third and fourth characters must be one of the following:
H9, HC, HD, HF, HG, HH, HJ, HK, HL, HM, HN, HP, HQ, HR, HT, HV, HW, HX, J1, J2, J3, J4, J5, J6, J7, J8, or J9