He Giveth More Grace is a song featured on Don Moen’s new album Hymnbook.
Moen speaks about his affection for the song here.
The hymn lyrics are written by Annie J. Flint.
I think the refrain in the verses below can also be a fourth verse. Maybe they started that way.
The lyrics:
1.
He giveth more grace when the burdens grow greater,
He sendeth more strength as the labors increase;
To added afflictions He addeth His mercy,
To multiplied trials He multiplies peace.
Refrain:
His love has no limits, His grace has no measure,
His power no boundary known unto men;
For out of His infinite riches in Jesus
He giveth, and giveth, and giveth again.
2.
When we have exhausted our store of endurance,
When our strength has failed ere the day is half done,
When we reach the end of our hoarded resources
Our Father’s full giving is only begun.
Refrain
3.
Fear not that thy need shall exceed His provision,
Our God ever yearns His resources to share;
Lean hard on the arm everlasting, availing;
The Father both thee and thy load will up bear.
Refrain
This isn’t Moen’s simple rendition, but it’s hard to complain about a room full of Gaither performers.
mgpcpastor's blog 
Greetings from Wordwise Hymns. Yes, most of the poem you quote came from the pen of Annie Johnson Flint. And yes, in one musical arrangement, the stanza “His love has no limits” is used as a refrain. However, I’m curious about where the stanza beginning “Fear not that thy need…” came from. I have books of Miss Flint’s poems going back to the 1920’s–at least two of which contain the poem–but not the other stanza. Nor does it sound like her. She was a very skilled poet, and “upbear” is rather awkward. I’d appreciate finding out where the added stanza came from. God bless.
Robert, I’ve got no idea where the extra verse comes from.
I see you’ve already poked around a few places that have published it (like mine).
Maybe Don Moen knows.
If you ever solve the mystery I’ll look forward to reading about it on Wordwise Hymns.