I think you must be
The title makes sense because
stable can be a synonym for secure.
In original form, I'm a refuge for beasts.
A stable is where beasts might find refuge.
Cut off my head, and I can hold forth a feast.
A table can hold a feast.
Remove it again, and my skills I will show.
One who is able has many skills.
Do so once more, and to me train drivers go.
Apparently this one's an American thing: BLE.
And in conclusion, though it seem rather odd-
Tie my first heads to my tail, and I shall be favored of God.
Perhaps this means blest (an alternative form of blessed).