Yes, it can run out of fuel, but it will NEVER EVER break(it will, however, burn in fire or lava.)! That's a promise for lifetime!
And if you possibly got some spare diamonds at hand, or just recently crafted some, you can now make an efficient and economic use of them:
Just combine them with the standard version of the D-765 Mining Drill and you will get an amazing device called the D-765 "Diamond Drill", whose mining speed is even faster than the speed of light!
You say it isn't? Of course it is! Do you think we would ever lie to you?!
This tool may be charged using a Generator of any kind or MFE/MFSU/BatBox. Alternatively, it can receive power from a Bat-Pack.It can also be recharged by right-clicking while holding a battery (hold right-click until it fully charges)