How can I get the LogCat before my phone restarts?
If the reboots are caused by kernel panics (sometimes the case), you can get the last_kmsg file. It's located at /proc/last_kmsg. This file gets reset every time you restart your phone, so you'll have to grab it soon after a reboot.

Look at the bottom of the file to see why the phone is rebooting. If it's a normal shutdown from an app, it may point to the app that initiated the shutdown. If it's a kernel panic, hopefully it'll tell you what's happening.