My LG enV VX9900 keeps turning off whenever I try to make a call. However, I can receive calls and send and receive texts.

If your phone is battery gets low for a short period of time then replace your phone battery, it is faulty or not fuctioning well. You can text or recieve calls but it may not take longer and when you try to make a call it suddenly shut down. So it is better to replace your battery with a new one to solve your phone problem.