The most common and most likely answer to this crossword clue is the 3 plus 4 letter word LET DOWN
I've seen this crossword clue in The Daily Telegraph
L
E
T
D
O
W
N
More clues leading to the result LET DOWN
- The French city hosting duke is disappointed
- Disappointed officer covers Estonia’s premier with feathers
- Disappointment making one lower
- Allow insulating material is a disappointment
- Disappointed and allowed to drink in one
- Fail to back up lease, depressed
- Lengthen lease, in writing
- Disappointed — at being dropped?
- Girls this disappointed could change to become strong-willed
- Diamonds buried in eastern settlement by large desert
Buddy explains!

The straight part
We know that "Fail to back up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fail to back up = let down.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does LET DOWN mean?
LET DOWN noun- A disappointment or anticlimax.
- The neurohormonal release of milk in dairy cows or in breastfeeding human mothers.