The most common and most likely answer to this crossword clue is the 8 letter word OBDURATE
I've seen this crossword clue in The Times
O
B
D
U
R
A
T
E
More clues leading to the result OBDURATE
- A doubter, awfully hard to persuade
- Stubborn old boy expected to hold rodent
- Make a speech about British — some of the French hard to persuade
- Dogged alumnus expected to harbour traitor
- Convert a doubter not easily swayed
- Determined a doubter will convert
- Pig-headed old boy taking time to admit “game over”
- Throw out bread that’s hard
- Out getting bread mix, deaf to all advice
- Half-baked bread out, becoming hard
Buddy explains!

The straight part
We know that "hard to persuade" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hard to persuade = obdurate.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 OBDURATE mean?
OBDURATE verb- To harden; to obdure.
- Stubbornly persistent, generally in wrongdoing; refusing to reform or repent.
- Physically hardened, toughened.
- Hardened against feeling; hard-hearted.