3G problem

My wife got a replacement phone from eBay recently (due to lack of cash) and picked a LG Vortex (Verizon). The phone works great and there are no issues except for 3G. When the phone boots the 3G icon shows in the status bar and everything works but after a while the icon disappears and she cannot get on anything like the Internet, Facebook, or Play Store. I go into settings and everything looks good and there is nothing that I need to change. I had unchecked and rechecked every box I could and still nothing. WiFi works good when on but this 3G thing is getting annoying as I don't know what else to try. Any ideas?