Without wanting to turn the discussion too heavy or technical, I think the passage where Galatians 6:9 is found is actually talking about not growing weary in teaching others.
6 Let him that is taught in the word communicate unto him that teaches in all good things. 7 Be not deceived; God is not mocked: for whatsoever a man sows, that shall he also reap. 8 For he that sows to his flesh shall of the flesh reap corruption; but he that sows to the Spirit shall of the Spirit reap life everlasting. 9 And let us not be weary in well doing: for in due season we shall reap, if we faint not. 10 As we have therefore opportunity, let us do good unto all men, especially unto them who are of the household of faith. 11 You see how large a letter I have written unto you with mine own hand.
Verse 6 could be interpreted a number of different ways, but I take "Let the one being taught in the word share (i.e. have shared experience) with the one teaching in all good things" to refer to simply not denying others of teachings that we are in a position to give them, even if doing so is a lot of work sometimes. This is why he says in verse 11, "You see what large letters I write to you." Paul was saying here that he was constantly pouring out his life in giving himself to teaching others, and writing large letters to the churches to that end.
It is motivational in a way, regardless of what our calling is, but I do think teaching is especially in view here, and most certainly can wear a believer out when you are at it all the time. It's mentally exhausting.