@omie19: +1 on saving contacts to the external SD card, just to have a copy handy, especially before undertaking anything as drastic as a factory reset.
@chetqwerty: for those who use Gmail, synchronizing contacts there makes sense. Others, including the OP, may find that other options work more effectively for them. In my case a goodly number of the contacts are on an Exchange server, so they're already backed up elsewhere. There are a couple dozen that have been directly entered on the phone, and those are happily synchronizing with Backup Assistant at the moment. There are also still quite a few on other platforms, and I will probably end up consolidating everything but the existing Exchange stuff into a private cloud-based service that has a privacy policy I can accept.
As noted above, others may well find that a Gmail-centric solution is ideal for their needs, but it sounds like Gmail isn't going to be part of the mix for the OP, so Android's built-in ability to synchronize with that platform is unlikely ever to be of any use. For now, Backup Assistant is a viable, supported alternative, and that is the context of the original request.
@sbudaj: before you do anything as extreme as a factory reset, you might want to try running BA without WiFi enabled. According to the Verizon techs with whom I spoke, attempting to run it across another network can sometimes create issues. That said, I have WiFi on almost all the time and it's been working fine for several weeks now, so this is more of a troubleshooting tool than a long-term solution.